Supermassive singularity the cause of the Big Bang?

[Marcus Gross]

OK so, I was wondering could the reason that our universe was in a hot dense state prior the the Big Bang Be because of it was actually a huge singularity that had no more mass to swallow up?
And what caused this is that a type of matter or subatomic particle interacted with a different matter or subatomic particle to cause the Big Bang?
If that is so, how many times has this happened?

 

[Orodruin]

No. Based on your post I don’t think you understand what ”singularity” means in this context.

 

[Ibix]

The Big Bang singularity and black hole singularities are rather different things. They both probably mean "general relativity doesn't work here", but they are different failures in very different solutions to Einstein's field equations. Black holes are surrounded by vacuum, whereas there's nowhere at all in the early universe that's vacuum. And our current best models expect black holes to eventually evaporate, not create new universes.

Black holes, incidentally, are the coldest things around - the more massive they are, the colder they are.

 

[cosmik debris]

Black holes, incidentally, are the coldest things around - the more massive they are, the colder they are.

If a massive black hole is cold then doesn't the CMB feed the hole and make it even colder? Therefore no massive black hole can ever evaporate by Hawking radiation.

Cheers

 

[phinds]

If a massive black hole is cold then doesn't the CMB feed the hole and make it even colder? Therefore no massive black hole can ever evaporate by Hawking radiation.

Cheers

That doesn't make sense. Black holes are only cold relative to other things. Right now they are colder than the CMB, so the CMB DOES feed the black hole, making it HOTTER not colder. At some point the CMB will be at a lower temperature than the CMB and Hawking Radiation will take over.

 

[Ibix]

If a massive black hole is cold then doesn't the CMB feed the hole and make it even colder?

It does. Black holes won't evaporate until the CMB cools below their Hawking temperature.

 

[Ibix]

making it HOTTER not colder.

Is that right? I thought Hawking temperature was inversely related to mass.

 

[phinds]

Is that right? I thought Hawking temperature was inversely related to mass.

Yes, it is. So what? The point is that right now large black holes are colder than the CMB so although they DO emit Hawking Radiation, it is swamped by the incoming radiation from the CMB and the BHs gets larger as a result (although not by an significant amount, I think). Eventually the CMB will be COLDER than the Hawking Radiation and the BH will start to shrink due to emitted Hawking Radiation. Exactly what you said in post #6

EDIT: Oh, I see. I was focusing on size (and confused it with temperature), you were focusing on temperature (and were not confused ). The point, which we both agree on, is that BHs DO eventually evaporate.

 

[cosmik debris]

That doesn't make sense. Black holes are only cold relative to other things. Right now they are colder than the CMB, so the CMB DOES feed the black hole, making it HOTTER not colder. At some point the CMB will be at a lower temperature than the CMB and Hawking Radiation will take over.

Well I think that was my point. Ibix said colder you said hotter. Which is it?

Cheers

 

[phinds]

Well I think that was my point. Ibix said colder you said hotter. Which is it?

Cheers

Colder. For a while. The point is that you were wrong to conclude that the BH can never evaporate. See my post #8

 

[Ibix]

Well I think that was my point. Ibix said colder you said hotter. Which is it?

The mass increase from absorbing CMB radiation is small in absolute terms, but the mass loss from Hawking radiation is even smaller. So the black hole grows and cools. But it doesn't cool as fast as the CMB. So in billions of years the CMB will overtake the black holes as coldest things, and net mass loss from the holes will set in, eventually leading to them evaporating entirely.

Always assuming we don't find this is all nonsense when we get quantum gravity working properly.

 

[phinds]

The mass increase from absorbing CMB radiation is small in absolute terms, but the mass loss from Hawking radiation is even smaller. So the black hole grows and cools. But it doesn't cool as fast as the CMB. So in billions of years the CMB will overtake the black holes as coldest things, and net mass loss from the holes will set in, eventually leading to them evaporating entirely.

Always assuming we don't find this is all nonsense when we get quantum gravity working properly.

Oh, it will take a LOT longer than that. In fact, compared to the amount of time it will take, billions of years is not even a rounding error.

 

[Buzz Bloom]

In the context of this thread, does anyone know of any thought experiment that describes a possible way for Hawking radiation to be observed some time prior to the time when the temperature of a black-hole will be warmer than then the CMB temperature.

 

[phinds]

In the context of this thread, does anyone know of any thought experiment that describes a possible way for Hawking radiation to be observed some time prior to the time when the temperature of a black-hole will be warmer than then the CMB temperature.

If you could maintain in position outside the EH with a very narrow-focus detector pointed at only a part of the EH, I don't see why it would be any problem. The tricks would be the sensitivity of the detector and the ability for it to maintain position. Also, it would have to be done with a BH that did not have infalling matter since even a trivial accretion disk would likely swamp the Hawking Radiation.

EDIT: Hm ... there's another complication. The detector could be picking up photons / cosmic radiation / whatever, that had been flung AROUND the EH. Guess it's all a bit tricky.

 

[Ibix]

In the context of this thread, does anyone know of any thought experiment that describes a possible way for Hawking radiation to be observed some time prior to the time when the temperature of a black-hole will be warmer than then the CMB temperature.

Far-fetched, but - make a small black hole whose Hawking temperature is comparable to the CMB temperature.

 

[Arman777]

In the context of this thread, does anyone know of any thought experiment that describes a possible way for Hawking radiation to be observed some time prior to the time when the temperature of a black-hole will be warmer than then the CMB temperature.

I think you are talking about the PBH's . In the early universe PBH has a mass of

$$M_{PBH}=10^{15}(\frac {t} {10^{-23}})g$$

In this sense, the black holes which produced earlier will have smaller masses an evaporate faster. And they will produce gama rays and emit some materials.

Hence, we should have limits on the density of the PBH's so that **they would not disturb the CMBR** or the **photon-baryon ratio** or many other things.

So to answer your question. Yes, we have an upper limit on the PBH density so that it cannot disturb the CMBR. And its $<10^{-21}$ for a mass range of $10^{11}g$ to $10^{13}g$

Or in other words if the PBH density was larger than this value then it would affect the CMBR.

For smaller masses than the given above, we have different kind of constraints to match the observable results.

 

[Buzz Bloom]

If you could maintain in position outside the EH with a very narrow-focus detector pointed at only a part of the EH, I don't see why it would be any problem.

Hi phinds:

I tried to come up with a thought experiment similar to this but the problem I could not resolve is that for any BH of a size with any reasonable likelihood that it would be be discovered, its temperature would be so much lower than, that of the CMB that the CMB radiation would completely obscure the Hawking radiation. What I found was that the size of a suitable detector would be so much larger than the BH it would not be able to be screened from the CMB even it it somehow it's screen was itself made colder than the Hawking radiation.

How does your idea avoid this?

Regards,
Buzz

 

[Buzz Bloom]

Far-fetched, but - make a small black hole whose Hawking temperature is comparable to the CMB temperature.

Hi Ibix:

Would such a small BH exist today or in the future? Is it technically possible to "create" such a BH? If so, would it be possible to detect it from a distance of the same order of magnitude similar to the size of the Milky-way?

Regards,
Buzz

 

[Buzz Bloom]

I think you are talking about the PBH's .

Hi Arman:

Am I correct in that all PBHs (if any ever did exist) are no longer in existence?

ADDED

I am a bit confused by your equation.
M_PBH = t × 10⁴⁸ g
where t is the Kelvin temperature.

This is saying that the mass is proportionate to the temperature rather than inversely proportional.

Regards,
Buzz

 

[phinds]

... for any BH of a size with any reasonable likelihood that it would be be discovered ...

You asked for a thought experiment. In my thought experiment, the BH has already been discovered.

 

[Buzz Bloom]

You asked for a thought experiment. In my thought experiment, the BH has already been discovered.

Hi phinds:

Thank you for responding with your thought experiment. I apologize for not being clear regarding discovery limitations on size with respect to my own attempt at a thought experiment. Unfortunately I cannot find my notes for this exercise, but I remember that that the mass of the BH was assumed to be about 3 solar masses based on a post in another thread:

https://www.physicsforums.com/threa...a-search-for-nearby-black-holes.940652/page-2
post # 40 Chronos
The smallest known black holes tip the scales at around 5 solar masses. A few may even be as small as ~3 solar masses, but this is difficult to confirm. In any event, that is not nearly small enough to emit a detectable amount of Hawking radiation. For that, you need a subsolar mass black hole. Aside from PBH [primordial black holes], there is no known way [even in theory] for such tiny black holes to form.​

The Hawking radiation temperature for a BH of this mass is ~2.06 10^-8 K.
I used the formula

T ~ 6.169×10^-8 M_sun/M.​

in

https://en.wikipedia.org/wiki/Hawking_radiation​

after the text:

The black hole acts as a perfect blackbody radiating at this temperature.​

The event horizon radius for this mass is 8.85 km, based on

https://en.wikipedia.org/wiki/Black_hole#Event_horizon
r = 2.95 M/M_sun km.​

The peak wavelength of black body radiation at temperature T is ~140 km.

https://en.wikipedia.org/wiki/Black-body_radiation
λ_max ~= 2.9 × 10^-3 / T​

Thus an antenna to detect the Hawking radiation will need to be very roughly about 10 times bigger than the size of the black hole. I do not see how this could be done without the antenna being swamped by the CMB.

Do you see a way to get around this with respect to your thought experiment?

Regards,
Buzz

 

[phinds]

Do you see a way to get around this with respect to your thought experiment?

Nope. Looks like your quantitative analysis has shown me wrong.

 

[PeterDonis]

I do not see how this could be done without the antenna being swamped by the CMB.

Sophisticated signal analysis might still be able to see that the radiation is not a single black body but two black bodies at different temperatures.

 

[Arman777]

Hi Arman:

Am I correct in that all PBHs (if any ever did exist) are no longer in existence?

ADDED

I am a bit confused by your equation.
M_PBH = t × 10⁴⁸ g
where t is the Kelvin temperature.

This is saying that the mass is proportionate to the temperature rather than inversely proportional.

Regards,
Buzz

Any PBH that has $M_{PBH}<10^{15}g$ are evoparted by now.

Larger PBH can exist ($M_{PBH}>10^{15}g$) but they have constraints again due to the lensing effects and etc. So even they exist their denisty is again very low.

In the equation t is not tempature, its time in second.

 

[Arman777]

Hi Ibix:

Would such a small BH exist today or in the future? Is it technically possible to "create" such a BH? If so, would it be possible to detect it from a distance of the same order of magnitude similar to the size of the Milky-way?

Regards,
Buzz

The small black holes (PBH) can form in the early universe but I don't think its possible to create them now.

The problem with the PBH is that their density should be very low in small scales, or in theory so that they don't effect the nucleosynthesis, CMBR etc.

 

[Buzz Bloom]

Sophisticated signal analysis might still be able to see that the radiation is not a single black body but two black bodies at different temperatures.

Hi Peter:

That is really what I am hoping to someday see explained. I have made an effort to calculate the Signal (Hawking Radiation = HR) to Noise (CMB) Ratio (SNR) under certain assumptions regarding "sophisticated signal analysis", but unfortunately, my knowledge of this topic is very limited. One very important aspect which I have not been able to find is how to evaluate: What is the probability that a weak HR signal is actually present in a context of strong CMB noise, that is a very low specific SNR? Another aspect I am not able to evaluate is the extent to which a sophisticated frequency filter design can improve the SNR beyond that of a simple Coil Capacitor (CC) filter.

I cannot find my original notes, but I can (with quite a few hours of effort) redo my calculation of the SNR of a simple antenna with a CC filter if anyone is interested.

Regards,
Buzz

 

[Buzz Bloom]

In the equation t is not temperature, its time in seconds.

Hi Arman:

Can you please explain the role of time in the equation in which mass is proportional to time?

Regards,
Buzz

 

[Arman777]

Hi Arman:

Can you please explain the role of time in the equation in which mass is proportional to time?

Regards,
Buzz

I actually don't know about it. The equation actually comes from

$$M=c^3t/G$$ but I never find an article that explains why there's time.

 

[PeterDonis]

What is the probability that a weak HR signal is actually present in a context of strong CMB noise, that is a very low specific SNR?

I don't know that much effort has been put into this, because the predicted SNR is so low that even if it were detectable in principle, in practice it would need detectors well beyond our current ability to construct (for example, an antenna 140 km wide).

 

[PeterDonis]

The equation actually comes from

$$
M=c^3t/G
$$

but I never find an article that explains why there's time.

Where did you get that equation from?

 

[Arman777]

Where did you get that equation from?

https://arxiv.org/abs/0912.5297

 

[PeterDonis]

https://arxiv.org/abs/0912.5297

Equation 1.1? In that equation, ##t# is the time after the Big Bang the the PBH forms; basically the equation is saying that the more time has elapsed since the Big Bang, the larger a PBH formed at that time would be. This is because the more massive a black hole is, the less "dense" it is (where "density" here means "the mass of the black hole divided by the volume of a Euclidean 3-sphere with a surface area equal to the black hole's horizon area"--which is not the actual physical density of the hole, since a black hole doesn't have a well-defined density, but plays the role of a density in the authors' proposed model for PBH formation).

 

[Arman777]

his is because the more massive a black hole is, the less "dense" it is

I did no understand this part.