Planck Stars: Carlo Rovelli & Francesca Vidotto

[Naty1]

Nugso:
If you haven't read it, Feynman's book WHAT DO YOU CARE WHAT OTHER PEOPLE THINK?, 1988 or so, is a rather irreverent look at science...and some people Feynman meets assocated with it including Neil Armstrong and Sally Ride a/w the Challenger disaster commission investigation. You won't learn an awful lot about science, but if you like Feynman, you'll laugh out loud at some of his antics.

 

[Naty1]

A wide ranging discussion...good stuff...

Marcus, very nice descriptions and simplified of the Rovelli paper...thank you...

[But, ah, ahem, how do I say this... we don't do "nursery rhymes" in physics forums...[post #33] or do we?? I thought this is a SERIOUS forum requiring some measure of decorum. Seems you are on the left wing coast, maybe 'moonbeams causing minor affectations out there? ...whatever, can't we possibly apply a different title, maybe "physics ditties" or maybe "geek rhymes"...or "symphonic physics poems"... if you insist on musical accompanyment...Have you possibly relocated maybe, too close to Hollywood? ]I had four thoughts as I read through the discussions:
Hawkings Jan 2014 paper, which I assume is what MTD alluded to early in this discussion, cosmological big bounce relationship to the paper, which you covered, ADS/CFT type [volume area] information correspondence [just mentioned] and finally the Chandrasekhar and Tolman–Oppenheimer–Volkoff limit of neutron degeneracy pressure...which I recall are quantum based calculations...

So be really interesting if this paper turns out to be correct what 'settled science' may be revised! I find the apparent discordance with Beckenstein bound and holographic especially interesting, if there is one, since that result [a bit per Planck area] seems to pop out from several different mathematical and theoretical approaches.

Here is a brief snippet of that 2/2014 Hawking paper for those interested:

http://arxiv.org/abs/1401.5761

Information Preservation and Weather Forecasting for Black Holes
S. W. Hawking
(Submitted on 22 Jan 2014)

….gravitational collapse produces apparent horizons but no event horizons behind which information is lost. This proposal is supported by ADS-CFT and is the only resolution of the paradox compatible with CPT. The collapse to form a black hole will in general be chaotic and the dual CFT on the boundary of ADS will be turbulent. Thus, like weather forecasting on Earth, information will effectively be lost, although there would be no loss of unitarity.

This seems it might be a key test of what they Rovelli/Smerlack et al are doing:

They make a big point that the even at the smallest point of the bounce the "star" is still large enough to contain all the information which has fallen in and which it must deliver at the end, when it explodes back into the rest of the world.

For example:

http://en.wikipedia.org/wiki/Holographic_principle

The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon.

the above along the lines expressed by Berlin...

Leonard Susskind seems to believe information bits can be explained by strings...

Here is one prior post I made that expresses my reservations so far:

Leonard Susskind in his book THE BLACK HOLE WAR (his controversy with Stephen Hawking) has some really interesting insights on information and horizons...like the horizon of a black hole is "stringy"...it can be described in terms of quantum strings...and so hidden information is proportional to the total LENGTH of a string!...and Hawking radiation can be viewed as string bits breaking loose from just outside the horizon...due to quantum fluctuations...a perspective akin to virtual particles causing the Hawking radiation.

I thought we generally believed so far strings are extended objects rather than the point particles of the Standard model...is it possible such 'extended objects' density can be unbounded as Chronos suggests??

 

[marcus]

Naty, thanks for the variety of thoughtful comment! You touch on many points. As for the rhyme, call it a "mnemonic" if you like. It helps me remember that initial mass of 1/5 gigaton leads to lifespan equal to present age of (expansion phase of) universe---plus the all-important fact that natural processes (like a bounce) proceed with extreme slowness deep in the hole's potential well.

Like many rhymes it can serve as a memory aid, if you're so inclined.

I wanted to try a sample calculation going back to redshift z+1=20,000. Let's see what size starburst would have happened then. I just put 20000 in for S in Jorrie's "Lightcone" calculator, and a zero in for the number of steps so the table will be just a one-liner:
{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.000&20000.000&0.000001873&0.0000&46.177&0.002&0.003&3.21&659.18\\ \hline \end{array}}It turns out that corresponds to year 1873 of the expansion.

Now the lifespan of the hole goes as the cube of the initial mass. In conventional Hawking model, one second corresponds to 228 metric tons. In the RV version that initial mass gives 0.65 seconds. The RV lifetime is 65% of the conventional (the thing bursts before it is completely evaporated).

(1873 years/.65 second)^.33333 * 228 tons = 1,025,000 tons

By comparison, again with the RV model, lifespan of 370,000 years implies initial mass of
(370000 years/.65 second)^.33333 * 228 tons = 5,971,000 tons ≈ 6 million tons

Very roughly, if you increase redshift by a factor of 20 (in this range of years) then the size of the gamma ray burst is decreased by around a factor of 6. From 6 million down to one million. That is how it works out in the early years preceding the emission of the CMB ancient light that we study today.

My intuition, and perhaps that of others as well is that since we observe the CMB with resolution of about one degree of angle, corresponding to about 1 million lightyears on the surface of last scattering, and these possible gamma bursts from primordial BHs are comparatively small, they would not leave an imprint at the million light year scale on the surface of last scattering. In other words they would not leave a visible imprint on the microwave sky.

Just wanted to buttress that with some numbers.

It would in any case have to be a mechanical disturbance, the gamma ray LIGHT would presumably be blocked by the opacity of universe before year 370,000. And any that was recent enough not to have been blocked would not be redshifted enough to blend in with CMB. It would still be x-ray or gamma. So we are just considering mechanical disruption of the surrounding gas by a comparatively small explosion (nowhere near the size of astrophysical GRB).

I don't know of any professional author who thinks primordial black hole (PBH) explosions could have left a detectable imprint on the microwave background. This may be why.

 

[Haelfix]

I'm going to reiterate my yearly plea to first learn the basics before discussing advanced physics concepts. That it would prevent all sorts of false claims from being ascribed to a paper that most assuredly does not make them.

That learning the basics will prevent very simple mistakes, like believing a black hole can hawking radiate and evaporate in the early universe (it's actually the opposite).

That physicists don't use units like kilotons. That there is no sense of talking about astrophysics size black holes as a dark matter candidate. That terms like information singularity have no operational meaning in physics. That talking about turbulence and super compressing matter in the context of inflation is word salad.

Gentlemen, I'm sorry to be rude but you are badly mangling a lot of physics In this thread.

 

[marcus]

...like believing a black hole can hawking radiate and evaporate in the early universe (it's actually the opposite)...

Good point! If the surrounding temperature is too high the thing can't evaporate. Since we are talking about primordial BH of around a billion kg (i.e. million metric tons) I will have to check to see what their Hawking temperature is compared with the universe temperature at the relevant redshift.

BTW What's wrong with using the mass equivalent of energy as a measure of energy?

Or what is wrong with expressing the mass of a black hole in kilograms?

A metric ton is simply 1000 kg. A million tons is a billion kg. Megaton is easier to say than Gigakilogram, or Teragram, or billion kilogram.

 

[marcus]

According to the Rovelli Vidotto model, what are the lifetimes of a sample of PBH (as long as the surrounding temp is not so high that the thing has trouble evaporating?) and also,what are their Hawking temperatures?

First, for a one Megaton (i.e. billion kg) PBH the temperature is
hbar*c^3/(k*8pi*G*10^9 kg) = 1.227e14 kelvin = 122.7 trillion Kelvin .

the conventional Hawking lifetime of such a thing is (10^6/228)^3 seconds in years = 2674 years
and the RV lifetime is 65% of that .65*2674 years = 1738 years

Recall that was roughly the lifetime I got when I wanted one that would blow at redshift 20,000 (as a kind of benchmark). At that time the universe temp is about 20000*2.76 Kelvin.
so the PBH is going to have no trouble evaporating. Its temp is in hundreds of trillions of K and the surrounding universe is cold by comparison: less than 100 thousand K.

Now suppose we want a PBH which bursts right around year 370000, when the universe became transparent to light and the CMB that we now see was emitted. That is going to be SIX Megatons. Because

(370000/1738)^.3333 = 6. does anybody have questions about this? The lifespan goes as the cube of the mass.

On the other hand the TEMPERATURE is inversely proportional to the mass. So we just have to divide the benchmark temp by 6:
122.7/6 = 20.5.
So that sample PBH has a temperature of around 20 trillion Kelvin. And for nearly all its 370,000 year lifetime the surrounding temperature is much MUCH lower. For instance it is only 3000 Kelvin in year 370,000.
So that sample PBH also will have no trouble evaporating.

 

[Haelfix]

So a good undergraduate unit for discussing mass is the kilogram. In twenty years of physics The only time I've ever seen tons utilized is when we discuss nuclear explosion yields, which is some bizarre historical accident and essentially a ridiculous unit.

For discussing astrophysics masses, an appropriate unit would be a solar mass. For microscopic black holes, something like the mass of a proton or something expressed in electron volts.

Primordial black holes of relevance to astrophysics have lifetimes that are many times the age of the universe. Primordial black holes of relevance to particle physics have essentially disappeared early on in the lifetime of the universe.

For dark matter candidates, microlensing experiments have essentially ruled out primordial black holes that are lighter than a certain threshold and gamma ray experiments provide a lower bound as well, which leaves a very small window on possible sightings. In any event, none of those types of pbhs would decay in the early universe, as it was simply too hot and they were absorbing Cmb photons at the time. Instead their lifetimes are roughly the age of the universe, for instance asteroid size objects and the like.

 

[marcus]

To summarize what I've been saying about lifespans of PBHs (primordial black holes) in early universe (according to Rovelli Vidotto "planck star") model.
First keep in mind that for PBH, in this discussion, a convenient mass unit is 10⁹ kg, which I'm calling a megaton (that is, a million metric tons).

To visualize that mass, it is the mass of a cube 100 meters on a side which is standard density (density of water). So the mass of a small asteroid, or a standard density cube the size of a football field.

Mass of PBH     Lifespan        when they burst
1 megaton       1700 years         redshift ~ 20,000   distances 1/20000 of size now
6 megaton      370,000 years       emission of CMB ancient light  redshift 1090
200 megaton   13.9 billion years   present-day era

For further reference, to make the mass additionally concrete, 1000 megaton is the mass of a standard density cube which is 1 kilometer on a side. Roughly speaking the mass of a medium size asteroid. A PBH of that mass would not be expected to burst for a very long time. Since lifespan goes as the CUBE of the mass, and it is FIVE times the mass of PBH which lasts until present era, the 1000 megaton PBH would last 125 times the present age of expansion.

So a good undergraduate unit for discussing mass is the kilogram. ...


For dark matter candidates,..

In any event, none of those types of pbhs would decay in the early universe, as it was simply too hot and they were absorbing Cmb photons at the time...

Hi Haelfix, I'll keep in mind your concern about units. In fact I am looking for a convenient unit of mass that could be visualized by high school students and lay-people and works in the context of the PBH I want to discuss, facilitates comparison with asteroids and cubes which reader can visualize.

I've found when you say billion and trillion too much, listener's eyes glaze over. So I'm trying out megaton.
Most of these people weren't even born yet when the old 1950s cold war buzz prevailed about "kilotons of TNT equivalent" so I don't think they will be bothered by thinking too much about TNT high explosive if we don't make a point of suggesting it. Just think about asteroids and big ice cubes.

You mentioned "dark matter candidates". We are not talking about "dark matter candidates" here. I've been interested in hearing about the sterile neutrino as a possible DM candidate. But that's another topic.

The PBH being discussed here spend most of their lifespans in a universe that is much lower temperature than they are, so they are free to evaporate. Your concern about the surrounding temperature being higher than the relevant BH hawking temperature is unnecessary in these cases.

You mention absorbing CMB photons. These were emitted when the universe temperature was about 3000 Kelvin, so you are referring to an early universe period after that, when the ambient temp was 3000 or LESS, and CMB photons already exist. The PBH we are talking about are hotter than 3000 Kelvin by many orders of magnitude. So ambient temperature would hardly interfere with evaporation.

Thanks for your comment. Needless to say, it's very helpful to have additional discussion!

 

[Haelfix]

Sorry, earlier comments in this thread were about dark matter. Mtd2s question was concerning the effect of PBHs on the cmb spectrum.

The answer is those black holes do not evaporate in the early universe. The only type of PBH that has sufficient mass range to appreciably influence the CMB are essentially dark matter candidates, who's mass range puts them around the age of the universe or so.

 

[marcus]

Sorry,..

No problem! In fact we did comment about PBH as dark matter earlier in thread, and then disposed of that.

What I'm interested in PBH as candidates for, and what Rovelli and Vidotto are talking about, is PBH as source of short gamma ray bursts, which are observed. According to Cline et al they don't have an isotropic distribution in the sky, suggesting they originate in our galaxy.

As I recall few come from the direction of galactic center and most actually come from the sector *opposite* galactic center which should have some cause LOCAL to the galaxy, perhaps something to do with the arm structure of the galaxy.

There is a suggestion that these short or very short bursts, unlike longer bursts, are not BEAMED. They arise IOW from a spherically symmetric explosion--so by a significantly different mechanism from the larger more distant longer-duration GRB.

Anyway we are not talking about "dark matter candidates" at this point.

I'm not sure what you mean by "influence the CMB". I don't think there is ANY reasonable chance that what we are discussing could influence any observable feature of the CMB ---and have been trying to convince MTd2 of this whenever he has brought up the possibility :^D

So I am glad that you agree with me on that, at least in general terms.

 

[marcus]

To re-iterate for clarity, what we are talking about are phenomena that could be observed at gamma or x-ray wavelengths if you assume the Rovelli Vidotto model of black hole.

So it is a possible test of the new RV model of BH, the "planck star" model as applied to primordial BH in this case. The model is interesting, different in significant ways, and could of course be wrong. We need observations to tell.

In order to talk about this you need to know the BASICS of this new BH model. In particular that it looks like a conventional BH for most of its lifetime but that its lifespan is only 65% as long for the same initial mass.

It evaporates by Hawking radiation at the same rate as a conventional BH of the same initial mass until its mass has dwindled to about 70% of initial (which takes about 65% of conventional lifespan) and then it blows up in a gamma burst. These are the short or very short GRB which could be studied.

Their energy is predicted by the theory and depends on when they exploded. Those that exploded in the past would have calculably less energy. Those exploding in the approximate present would have an energy mass-equivalent of about 140 megaton, or if you like 1.4 x 10¹¹ kg.
Folks can multiply that by the speed of light squared to get the ergs or joules if they like.

 

[Paulibus]

I'm convinced that the Rovelli-Vidotto model of a Black Hole, and how the gravitational collapse of such can be frustrated by a singularity-preventing bounce, is a landmark paper; it has really interesting implications for both Blackholery and Cosmology.

But despite having looked at (and not properly understood ) many of the technical background papers mentioned in this thread, I find the root cause of the bounce difficult to fit into my primitive background of Physics:

...The bounce is due to a quantum-gravitational repulsion which originates from the Heisenberg uncertainty, and is akin to the "force" that keeps an electron from falling into the nucleus. The bounce does not happen when the universe is of Planckian size, as was previously expected; it happens when the matter/energy density reaches the Planck density. In a matter dominated universe ... the bounce can happen at large values of the size of the universe: using current cosmological estimates, quantum gravity could become relevant when the volume of the universe is some 75 orders of magnitude larger than the Planck volume. Quantum gravity effects do not happen only over Planck volumes.

This introduction to the key point of the whole scheme is on p. 1 of the Rovelli-Vidotto paper. I'd appreciate some fleshed-out, low-level help in better understanding how this "quantum-gravitational repulsion" arises.

 

[marcus]

I'm convinced that the Rovelli-Vidotto model of a Black Hole, and how the gravitational collapse of such can be frustrated by a singularity-preventing bounce, is a landmark paper; it has really interesting implications for both Blackholery and Cosmology.
…
I find the root cause of the bounce difficult to fit into ...

Hi Paulibus, good to hear from you! I agree about the papers likely landmark role. I also share your sense that the bounce needs an intuitive explanation. I'll try to whittle away at that problem.

Notice that bounce is not unique to LQG, there are other cosmological models, whether classical or to some extent quantum, where a bounce occurs. As I recall there at least one "nonsingular" cosmologies review paper that lists and discusses several bounce models besides Loop. It would be too distracting to get into that so I will focus on Loop.

I can get SOME intuitive sense by thinking about electron degeneracy pressure that keeps ordinary matter from collapsing into neutron matter. I relate that in a general sort of way to Uncertainty Principle. Nature doesn't like being pinned down. Maybe geometry is analogous to matter in that regard, and resists being pinned down. Maybe geometry insists of some ultimate margin of freedom to be uncertain. But that's too vague, I want us to be able to contemplate something more quantitative.

Focussing just on Loop gravity, the bounce first appeared in cosmology around 2001. And in 2006 the original Loop cosmology dynamics were replaced by Ashtekar Pawlowski Singh improved dynamics, so then the bounce had to be checked all over again---at length. they were never sure it was going to occur, so kept exploring different cases. I get the impression that central people like Ashtekar do not themselves have an intuitive understanding of why the cosmological bounce has turned out to be such a robust feature of their model. They have acted as if they were surprised when it surfaced in 2001 and still cautious about it in 2006. But that shouldn't make US give up on getting an intuitive sense of why it happens.

Notice also that they did not immediately carry the bounce idea over from Cosmology to Black Holes! I remember for years being frustrated whenever I examined a new Ashtekar et al paper and found that he was doing almost anything to avoid concluding that BHs bounced. All but a very few LQG people were reluctant to accept the "baby universe" idea and I think BH bounce was equated to "baby universes" in everyone's mind. So all but a few avoided the BH bounce idea.

One reason this paper is a landmark is because it analyzes a bounce that rebounds back into OUR universe rather than budding off a baby one. So in that sense it is the first "mainstream" Loop BH bounce.

So far I am just giving an impressionistic and personal account of background and context. I want to unpack some intuition about the actual phenom. But I'll take some time to think and make a separate post for that.

One path towards bounce intuition might be to contemplate the fact that in Loop gravity there is an absolute fundamental maximum on acceleration.
I think that translates into some other geometrical and thermodynamic limits. Say on temperature, or on "the force of gravity" whatever that means , or on certain gradients like the temperature gradient, density gradient, maybe also on curvature...

Suppose we first talk about the Loop gravity limit on acceleration. It seems so unintuitive that there such be a maximal acceleration! Maybe if we can get over that first (simplest) intuition hurdle it will be easier to accept that nature's geometry could bounce.

 

[marcus]

I'm convinced that the Rovelli-Vidotto model of a Black Hole, and how the gravitational collapse of such can be frustrated by a singularity-preventing bounce, is a landmark paper; it has really interesting implications for both Blackholery and Cosmology.
…
I find the root cause of the bounce difficult to fit into ...

One path towards bounce intuition might be to contemplate the fact that in Loop gravity there is an absolute fundamental maximum on acceleration...

Acceleration is interesting partly because of the "equivalence principle" that if you put a physicist in a box and uniformly accelerate the box then he can't tell the difference between that and the box sitting in a uniform gravitational field.

So if you put two physicists in the box and accelerate it, the forward one feels like he's upstairs and the aft one feels like downstairs, and their clocks run at slightly different rates. Nature functions slower downstairs. There's also the Unruh temperature thing, with acceleration. So establishing a maximal acceleration relates to a lot of things: time rate gradient, gravitational potential gradient…

Why should there be a maximal acceleration? It seems so unnatural! Could this paper be wrong?
What's the intuition behind this? (You may know the paper, Paulibus. But it could be worth our reviewing.)
http://arxiv.org/abs/1307.3228
Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
Carlo Rovelli, Francesca Vidotto
(Submitted on 11 Jul 2013)
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Comments: 4 pages, 1 figure

Only 4 pages, how hard can it be?

 

[marcus]

In figure 1 the smaller the shaded area the more extreme the acceleration. You can see that the probe is coming in from the right almost at speed of light (i.e. nearly parallel to the incoming 45 degree line) decelerating madly and zooming off to the right again approaching speed of light (the outgoing 45 degree line).

Loop has an area minimum (one of the earliest results) which could enter into play here.

And why shouldn't there be a maximal acceleration after all? It has even been expected for several decades based on theoretical considerations.

Here's from conclusions on page 4:
"Maximal acceleration appears to cure strong singularities (in the terminology of [29, 30]) such as big bang, big crunch, black holes, as well as more exotic ones…"

Still unresolved but have to go to a rehearsal. Back later to look at this some more. Hope you have a look and find parts of it helpful.

 

[Paulibus]

Thanks for the full replies and pointing me at the interesting Rovelli-Vidotto paper on "Evidence for Maximal Acceleration" which I was unaware of. But I run aground easily; so far I have trouble checking the dimensions of even the simplest of their equations, e.g. [18], perhaps because they cleverly simplify by setting c = 1. I do wish this wasn't accepted practice.

Your comment in post #74 about physicists in an accelerated box set me puzzling also. The principle of equivalence between acceleration and gravitational fields extends also to their degree of uniformity, I hope. So the environment inside a uniformly accelerating box (say with chairs to stay relatively put in) is not quite equivalent to the radially not-quite-uniform gravitational field of the Earth. Inhomogeneity must be what makes Nature appear to function slower downstairs than upstairs. Maybe that's why Hell looks so eternal to those in Heaven? Gravitational red-shifts are, I think, caused by field gradients rather than uniform fields. Or are they?

But all this is just displacement activity. I'll get back to trying to understand Rovelli-Vidotto -- good stuff; I have a daughter Frances.

 

[MTd2]

Let me rephrase a bit my argument.

I suppose that primordial black holes would be caused by non uniformity of the inflaton process. Suppose that a volume A inflates, for a short moment, at a slightly lower than a volume B surrounding it. The area surrounding A will work like a compressor around B. It will squeeze the matter at A to a small black hole.

I also supposed that this non uniformity of the inflaton makes itself turbulent. So, I estimated how the rate of formation of primordial black holes, during inflation, would fall with the cooling of the universe at my post #51. It falls with the inverse of the 4th in relation to the temperature. Given that the temperature falls fast I supposed that the smallest ones would be the ones at the beginning, but I conjectured that the total volume of black holes would be bigger for those formed in the beginning of inflation, since we are talking about an overall adiabatic expansion of the universe, the rate of formation would fall faster then the fall of temperature. But, also, the earlier black holes would evaporate faster due its small mass, which I think due the fast cooling of the universe during inflation, would be always bellow the background temperature.

This would affect the CMB by accoustic oscillations, like this:

http://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

Even though these very early black holes should have a very high frequency, they should, this is only I guess, leave a mark due amplification by inflation and very high z.

This process may explain apparent violation to cosmological principle, like this(?): http://en.wikipedia.org/wiki/Huge-LQG

And formation of matter\dark matter concentrations beyond what would be expected by this principle, by the scattering process of non homogenous inflation and mini black hole explosions.

 

[marcus]

Let me rephrase a bit my argument.

I suppose that primordial black holes would be caused by non uniformity of the inflation process.
...
This would affect the CMB by accoustic oscillations, like this:
http://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

Even though these very early black holes should have a very high frequency, they should, this is only a guess, leave a mark due amplification by inflation and very high z.

This process may explain apparent violation to cosmological principle, like this(?): http://en.wikipedia.org/wiki/Huge-LQG

And formation of matter\dark matter concentrations beyond what would be expected by this principle, by the scattering process of non homogenous inflation and mini black hole explosions.

Well this, as you indicate Daniel, is somewhat speculative. You are talking about mini primordial black holes (PBH) that may have formed during inflation and exploded promptly so as to be "amplified by inflation and very high z" so that they could have had an effect on "Baryon acoustic oscillations" and the like. Perhaps producing inhomogeneity at large enough scale to be visible in CMB.

I can't fault this as a speculation, nor does it contradict what I was discussing which was evidence of more massive longer lived PBH as gamma ray bursts (GRB) and as contributors to the gamma ray and x-ray background. Your idea is a completely separate subject of inquiry!

But we are talking about the Planck stars BH model with SLO-MO REBOUND replacing the "singularity". It is not clear to me how your conjectured effect on CMB could TEST this model. How would the disruption of CMB isotropy look any different with the Planck star PBH than with the conventional PBH?

If the imagined effect on CMB does not DISTINGUISH between conventional and Planck star model then it does not seem related to the topic of this thread. Or does it simply need a lot more quantitative/numerical work before you can tell whether it relates to the Planck star model or not?

 

[marcus]

... the interesting Rovelli-Vidotto paper on "Evidence for Maximal Acceleration"... But I run aground easily; so far I have trouble checking the dimensions of even the simplest of their equations, e.g. [18], perhaps because they cleverly simplify by setting c = 1. I do wish this wasn't accepted practice.

... the environment inside a uniformly accelerating box (say with chairs to stay relatively put in) is not quite equivalent to the radially not-quite-uniform gravitational field of the Earth. Inhomogeneity must be what makes Nature appear to function slower downstairs than upstairs. Maybe that's why Hell looks so eternal to those in Heaven? Gravitational red-shifts are, I think, caused by field gradients rather than uniform fields. Or are they?

... I'll get back to trying to understand Rovelli-Vidotto -- good stuff; I have a daughter Frances.

Hello to F, I hope her interests include some physics and or cosmology! They're good things for a young person to keep an eye on IMHO.

I'll have a look at equation [18] on the off chance I can help.

You are certainly right about radial inverse square being different from uniform, even though with a large enough radius the one can approximate the other. I believe gravitational redshift would still be caused by a uniform field, there is still a potential gradient (an idea of depth, a downstairs and an upstairs). I'd be embarrassed to learn I was mistaken about this, it seems so intuitive, but you might be right.

I think of the steadily accelerating box with the forward and aft (to use nautical terms) physicists who have been told by a duplicitous Experimenter that they are in a gravitational field. Upstairs sends a flash of light to downstairs and by the time it gets there the receiver is coming to meet it faster! So he detects a blueshift. And so on. This confirms their mistaken belief (suggested to them by the guileful Experimenter) that they are in a gravitational field.

 

[MTd2]

Or does it simply need a lot more quantitative/numerical work before you can tell whether it relates to the Planck star model or not?

There is, indeed, a need of numerical inference. But, I don't think these problems are not unrelated, indeed, since I cannot think there is any kind of "compressor" mechanism capable of producing small black holes with any range of masses, other than inhomogeneities during inflation as I described. You know that the smaller the black hole, the greater is the pressure for a given matter density.

Outside the inflation range, only a ~2-10 solar (outside this range, I am not aware of any process other than simply falling mass to a stellar black hole or black hole merging) mass can be compressed enough to form a black hole, as far as I can imagine.

So, I think both are related. Since, after the supposed numerical calculation, the abundance of primordial black explosions should be related to a given time of the inflation, where it was generated. So, studying both the CMB and the remains of explosions, should help to understand inflation, when it began, how much it lasted, among other things.

Do you have any other idea of how such black holes might be formed? I initially formed about quantum gravity fluctuations before inflation, but it seems that by CDT the universe becomes homogeneous at a very small scale, hundreds of plank scale, at least homogenous enough not to form a black hole

 

[marcus]

Daniel, a lot has been written about primordial BH, specifically as sources of gamma ray bursts and such-like high energy radiation. I think if one is interested in the possibility of visible disruption to the CMB caused by PBH explosions then one needs to start reading the technical literature on PBH. At this point it doesn't seem to have a specific connection with the Planck star BH model, so maybe a separate thread?

As a reminder, here's the reference to the paper Paulibus and I (hopefully others as well!) were considering:

Acceleration is interesting partly because of the "equivalence principle" that if you put a physicist in a box and uniformly accelerate the box then he can't tell the difference between that and the box sitting in a uniform gravitational field.

So if you put two physicists in the box and accelerate it, the forward one feels like he's upstairs and the aft one feels like downstairs, and their clocks run at slightly different rates. Nature functions slower downstairs. There's also the Unruh temperature thing, with acceleration. So establishing a maximal acceleration relates to a lot of things: time rate gradient, gravitational potential gradient…

Why should there be a maximal acceleration? It seems so unnatural! Could this paper be wrong?
What's the intuition behind this? ...
http://arxiv.org/abs/1307.3228
Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
Carlo Rovelli, Francesca Vidotto
(Submitted on 11 Jul 2013)
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Comments: 4 pages, 1 figure
...

Paulibus mentioned equation (18). I'll have a look and also anybody else's explanatory comment is welcome!

 

[MTd2]

I just want to know if these things can be generated. Existing mathematically may be just like talking about the reality of a Godel universe.

 

[marcus]

Paulibus, I put the c back into equation (16), as I believe you wished.
Also I think equation (5) says A = c⁴/(2a²)
So one can solve for a:
a = (c⁴/2A)^1/2
==quote==
Restoring physical units, we have a minimal nonvanishing value of the area
A_min = 4πGℏ/c³, …………..(16)

which, recalling (5), gives a maximum physical value of the accelerations

a_max= (c⁷/8πGℏ )^1/2…………..(17)
The existence of a maximum value of acceleration is of course something long expected in quantum gravity…
==endquote==

Paulibus you were right about their setting c=1 and removing all the c from the equations (16 thru 18), and elsewhere, but I have restored the c raised to what I think are the appropriate powers. So we ought to be able to find out what actually IS the max acceleration. It will be stupendously abrupt acceleration, I expect . Have to run some errands, but will get back to this later!

Francesca used to post here frequently and made a valuable contribution to BtSM forum as a PF member. Now we have her occasional research papers.

 

[marcus]

For continuity:
What's the intuition behind this? ...
http://arxiv.org/abs/1307.3228
Evidence for Maximal Acceleration…

... the interesting Rovelli-Vidotto paper on "Evidence for Maximal Acceleration"... But I run aground easily; so far I have trouble checking the dimensions of even the simplest of their equations, e.g. [18], perhaps because they cleverly simplify by setting c = 1. I do wish this wasn't accepted practice.

... I'll get back to trying to understand Rovelli-Vidotto -- good stuff; I have a daughter Frances.

(c⁷/8πGℏ )^1/2 unpacked for the google window's calculator is:

(c^7/(8pi hbar*G))^(1/2)

When I put that in the google window, I get

1.10924269 × 10⁵¹ m/s²

So if you put the appropriate power of the speed of light back into Rovelli and Francesca's expression for the maximal acceleration, the google calculator is able to parse it and gives back an acceleration in standard format.

Probably it is something an aficionado would recognize as "Planck acceleration" aka one Planck unit of speed per Planck time unit. Or that times a numerical factor of order one.

 

[marcus]

The introduction of the July 2013 "Evidence for Maximal Acceleration" paper has a brief paragraph that summarizes how the a_max derivation goes:

==quote page 1 of http://arxiv.org/abs/1307.3228 ==
... The key to our derivation relies on a core aspect of the covariant approach: the proportionality between generators of boosts and rotations [15]. This ties space-space and space-time components of the momentum conjugate to the gravitational connection and transfers the discretization of the area spectrum to a discretization of a suitable Lorentzian quantity, which, we show, is related to acceleration. The mechanism indicates the existence of a maximal acceleration. This, in turn, yields a bound on the curvature and on the energy density in appropriate cosmological contexts, supporting the results in loop quantum cosmology and for black holes…
==endquote==

It's easy to see that they were already anticipating results about the density maximum, the bounce, and the Loop black hole model, back in July 2013 when they were deriving the Loop acceleration max.

SO THERE ARE TWO things to become conversant with here: the discrete area spectrum and the boost-rotation proportionality. They are too technical for us to enter into detail explanation right now. Let's just be aware of them as keywords, and as essential features of Loop gravity.

The discrete area spectrum was one of the earliest results of LQG, going back to around 1990. It's constantly coming up in discussion and being applied (along with analogous discreteness results for some other geometric operators).

The proportionality between boost and rotation generators is here being used to link acceleration with area and as they said, to "transfer" the discreteness. That proportionality is associated with the basic function on which spinfoam dynamics is built, the so-called "Y map". I first recall seeing it in connection with some work by Eugenio Biachi around 2006 or 2007. The idea is we have two important groups SU(2) (basically spatial rotations) and SL(2,C) (basically spacetime symmetries, the Lorentz group). To take on DYNAMICS we have to map one into the other! Abstract groups are concretized by their matrix "representations" so we need an algebraic map from the SU(2) reps to the SL(2,C) reps. The Y map does this.
So Loop dynamics is built on it and ALSO it establishes that proportionality we were talking about.

Now for a moment everything becomes overly algebraic and a bit incomprehensible. I'll just quote some words from one of the many paper where Y map has appeared in the spinfoam literature during recent years. For a concise summary (minus explanatory background) one can refer to any of numerous papers. One I like is by Chirco, Haggard, Riello, Rovelli. E.g. have a look at page 6 of this:

==quote page 6 of http://arxiv.org/abs/1401.5262 ==
The dynamics of the theory is obtained mapping these states to unitary representations of SL(2,C). A unitary representation (in the principal series) [25] is labelled by a discrete spin k ∈ N/2 and a continuous parameter p ∈ R⁺ and the representation space is denoted H_(p,k). This space decomposes into irreducible representations of the SU(2) subgroup as follows

H_(p,k) = ⊕_j=k^∞H_j . . . . . (40)

where H_j is the (finite dimensional) SU(2) representation of spin j. Therefore H_(p,k) admits a basis |(p, k); j, m⟩ obtained diagonalizing the total angular momentum L² and the L_z = L⃗ · ⃗z component of the SU(2) subgroup. The map that gives this injection, and defines the loop quantum gravity covariant dynamics is given by

Y_γj→H_j^γ
|j,m⟩→ |(γj,j);j,m⟩ . . . . . . . . (41)

Here [the gamma] γ ∈ R⁺ is the Immirzi parameter.
….
….
On the image of the map Y_γ, the boost generator K⃗ and the rotation generator L⃗ satisfy
⟨K⟩ = γ⟨L⟩ . . . . . . . . (43)
as matrix elements.
==endquote==

I tried not too successfully to make the lowercase italic gamma visually distinguishable from the capital Y. Gamma is just a positive real number--it's used in constructing SL(2,C) Lorentz group representation matrices and it turns out to actually BE the proportionality we were looking for.

 

[marcus]

The Planck star (delayed rebound) model of black hole has several interesting things about it.

It resolves the "information loss paradox" because all the info comes back in a simple way, in a long-delayed bounce gamma ray burst (GRB)

It resolves the BH singularity with something physical (no infinities: a bounce).

It doesn't lead to bizarre complicated stuff (e.g. Leonard Susskind's "firewalls") that torment other BH models.

It doesn't get into the "baby universe" business--the rebound is back into OUR space, it does not create a new expanding region (which some earlier black hole bounce concepts depicted).

There are possible PREDICTIONS.
=================

This last point is important: the size of the explosion is not the same for all BH (as in the conventional Hawking evaporation model) but instead the explosion size goes as the cube root of the lifespan.

So that makes the issue of PRIMORDIAL black holes (PBH) crucial to testing the model. The model can be used to predict the energy of pbh GRB that we should now be observing if PBH of the required sized were in fact created in the early universe.

So we may have use for this REVIEW article about PBH by Anne Green. It will be published as the PBH chapter in a book on Quantum BH edited by a former Physicsforums poster named X. Calmet.

Useful review, could serve as source for Planck star discussion:
http://arxiv.org/abs/1403.1198
Primordial Black Holes: sirens of the early Universe
Anne M. Green
(Submitted on 5 Mar 2014)
Primordial Black Holes (PBHs) are, typically light, black holes which can form in the early Universe. There are a number of formation mechanisms, including the collapse of large density perturbations, cosmic string loops and bubble collisions. The number of PBHs formed is tightly constrained by the consequences of their evaporation and their lensing and dynamical effects. Therefore PBHs are a powerful probe of the physics of the early Universe, in particular models of inflation. They are also a potential cold dark matter candidate.
21 pages. To be published in "Quantum Aspects of Black Holes", ed. X. Calmet (Springer, 2014)

 

[Paulibus]

Marcus: thanks for restoring (in your post #84) the factor of c^7 in eqn. 17 of the Rovelli-Vidotto acceleration paper. The maximal acceleration is then easily remembered as roughly 50 orders of magnitude bigger than familiar g. It's reassuring to know that this fundamental limit to acceleration is too large to affect sports like aerobatics or drag racing!

I believe gravitational redshift would still be caused by a uniform field, there is still a potential gradient (an idea of depth, a downstairs and an upstairs). I'd be embarrassed to learn I was mistaken about this, it seems so intuitive, but you might be right.

You are probably right. Think of a photon that carries energy and therefore mass 'upwards' in a perfectly uniform gravitational field. The field exerts a force on this mass and work is done by the photon: force x distance. Work saps photon energy, reduces its frequency, increases its wavelength and red-shifts the photon. But I can't help feeling that this argument is somehow naive, and now I'm somewhat confused by the fact that photons can't just slow down, like vertically thrown objects. But Nature is cunning at extracting work, just as the taxman is at extracting payment.

Lastly, fore and aft; ok with me. I'm an ex Fireball yachtie.

 

[marcus]

Marcus: thanks for restoring (in your post #84) the factor of c^7 in eqn. 17 of the Rovelli-Vidotto acceleration paper. The maximal acceleration is then easily remembered as roughly 50 orders of magnitude bigger than familiar g. It's reassuring to know that this fundamental limit to acceleration is too large to affect sports like aerobatics or drag racing!

You are probably right. Think of a photon that carries energy and therefore mass 'upwards' in a perfectly uniform gravitational field. The field exerts a force on this mass and work is done by the photon: force x distance. Work saps photon energy, reduces its frequency, increases its wavelength and red-shifts the photon. But I can't help feeling that this argument is somehow naive, and now I'm somewhat confused by the fact that photons can't just slow down, like vertically thrown objects. But Nature is cunning at extracting work, just as the taxman is at extracting payment.

Lastly, fore and aft; ok with me. I'm an ex Fireball yachtie.

Six photos here, #5 in sequence is especially gratifying:
http://www.fireball-international.com
Specs:
http://sailboatdata.com/viewrecord.asp?class_id=2945
History:
http://www.fireball-international.com/the-boat/history/

Handling a light planing hull with more than enough sail area must surely be a good preparation for learning physics intuition. Misjudge and you get a dunking. Or so I guess. :^D

 

[Ken G]

I wonder what is the connection between uncertainty and the minimum quantum of action, h. You don't really need uncertainty to get degeneracy support if you have a minimum quantum of action, so it may be more the latter that is the analog of maximum acceleration. A maximum geometric curvature would connect to a minimum sized circle, and the connection between action and acceleration is that action associates with only the fundamental constant h and acceleration associates with the inverse square root of the product of h and G (I don't think c is of importance, it's just a kind of medium of exchange between the various scales, I think we could understand the situation just with h and G, action and gravity). So maximum acceleration seems to combine the minimum action h with a minimum of something else that associates with gravity. It reminds me of how many systems acquire a maximum kinetic energy when their action is minimal, we may have something here where a spacetime system acquires a maximum curvature when some generalized version of action reaches a minimum of the geometric mean of h and G.

 

[marcus]

The way I see it, that's the best post on this thread so far. It's really interesting. I've avoided posting for a couple of days so as not to "cover it" but leave it visible on the menu. what you suggest here is a line of research that somebody could do, analogous to that by Vidotto and Rovelli in the "Evidence for Maximal Acceleration" paper http://arxiv.org/abs/1307.3228 but about an action quantity instead of acceleration.

You refer to it as "the geometric mean of h and G" which is a nice way to think of the Planck length. BTW here's how I remember some of those natural units quantities, since my memory is not great and I can use a mnemonic now and then:
Obviously hbar∗c is energy∗length = force∗area
and the natural unit of force is c⁴/G (the one thing I have memorized).
So divide force∗area by force and you get hbar∗G
You say neglect factors of c, so I leave off the /c³ denominator.
So then the square root of that hbar∗G is the length.