B Do things that fall into black holes ever reach the singularity?

[docnet]

A Paradox of the black hole is that GR states the stationary observer experiences time dilation, while the inflating observer experiences no time dilation. By the time the infalling observer reaches the event horizon, an infinite amount of time passes for the other frame of reference. But black holes evaporate in a finite amount of time.. so do physical laws prevent anything from really reaching the event horizon?When black holes are created by implosion, does GR state the matter inside of the event horizon stays frozen at the time of implosion in time until the end of the black hole's lifespan? Relativity is a mind boggling concept.

 

[hmmm27]

The inductee is long gone by the time the photons emitted/reflected by same reach an outside observer.

 

[PeterDonis]

A Paradox of the black hole is that GR states the stationary observer experiences time dilation, while the inflating observer experiences no time dilation

Where are you getting this "paradox" from?

Also, I think you mean "infalling observer", not "inflating observer". Assuming that's true, it is incorrect to say that an infalling observer experiences no time dilation. A correct statement would be that the concept of "time dilation" does not even make sense for an infalling observer.

By the time the infalling observer reaches the event horizon, an infinite amount of time passes for the other frame of reference. But black holes evaporate in a finite amount of time.. so do physical laws prevent anything from really reaching the event horizon?

This is an old chestnut that has been answered many times here on PF. The short answer is that you are mixing up two different spacetime geometries. The "an infinite amount of time passes for the other frame of reference" is only true in the classical black hole geometry (and even there it has to be interpreted carefully since it's easy to be led into misconceptions), where there is no evaporation, the hole is eternal. In the spacetime geometry in which the hole can evaporate, because we are including quantum effects, it does not "take an infinite amount of time" according to a distant observer for an infalling object to reach the horizon; the distant observer sees the infalling object reach the horizon at the same instant he sees the hole evaporate, and can reconstruct from what he sees that the object fell into the hole before it evaporated.

When black holes are created by implosion, does GR state the matter inside of the event horizon stays frozen at the time of implosion in time until the end of the black hole's lifespan?

No. The imploding matter continues on inward until it reaches zero surface area and forms the singularity.

 

[docnet]

Where are you getting this "paradox" from?

Sorry, it may not be a paradox to a sophisticated physicist. I am not sure, maybe the right term is duality? I watched Leonard Susskind's lectures and he described that a person - Alice - doesn't notice anything different as she falls through event horizon. Leonard described a black hole which is so massive, it takes Alice a thousand years to cover the distance from the event horizon to the singularity, Alice will not notice anything different until the tidal forces rip her apart.

In the same time, the faraway observer sees Alice reaching the event horizon and becoming plastered and scrambled over the surface of the hole. Leonard said both cases are true, which seems like a puzzling paradox to me. But surely this must be a controversial theory in the field of theoretical physics.

Also, I think you mean "infalling observer", not "inflating observer".

yes, it was the autocorrect. an inflating observer would be puzzling.

This is an old chestnut that has been answered many times here on PF. The short answer is that you are mixing up two different spacetime geometries. The "an infinite amount of time passes for the other frame of reference" is only true in the classical black hole geometry (and even there it has to be interpreted carefully since it's easy to be led into misconceptions), where there is no evaporation, the hole is eternal. In the spacetime geometry in which the hole can evaporate, because we are including quantum effects, it does not "take an infinite amount of time" according to a distant observer for an infalling object to reach the horizon; the distant observer sees the infalling object reach the horizon at the same instant he sees the hole evaporate, and can reconstruct from what he sees that the object fell into the hole before it evaporated.

Ah.. that's an incredibly interesting insight I have not heard before. thanks for that. seems like that would even the tally.

Question: why does the imploding matter deserve a different explanation than the first? Instead of imploding into a singularity immediately, wouldn't the imploding matter form a singularity at the moment the black hole evaporates?

 

[PeterDonis]

Leonard said both cases are true

Susskind here is not talking about the classical GR model of black holes, or even about the simple Hawking model of an evaporating black hole taking into account quantum effects. Susskind is talking about a speculative quantum gravity model that he likes.

surely this must be a controversial theory in the field of theoretical physics

It is, although Susskind likes to claim that the controversy has been resolved (in his favor, of course).

Instead of imploding into a singularity immediately

It doesn't. It takes time, according to an observer falling in with the imploding matter, for the implosion to go from the horizon to forming the singularity.

wouldn't the imploding matter form a singularity at the moment the black hole evaporates?

There is a sense in which this is a valid description, but it's not one that is very intuitive. The singularity itself is not a place in space; it's a moment of time. That moment is to the future of all events inside the black hole's horizon. The formation of the singularity when the imploding matter reaches zero radius happens at this moment of time, at one location in space; and the final evaporation of the hole and the release of radiation outward towards distant observers, including light signals emitted by all objects that crossed the horizon, when they crossed the horizon, also happens at that moment of time, but at a different location in space. These two locations in space are opposite "ends", so to speak, of "space" at the moment of time of the singularity.

 

[docnet]

The singularity itself is not a place in space; it's a moment of time.

thanks for the food for thought :)

 

[Elias1960]

In the spacetime geometry in which the hole can evaporate, because we are including quantum effects, it does not "take an infinite amount of time" according to a distant observer for an infalling object to reach the horizon; the distant observer sees the infalling object reach the horizon at the same instant he sees the hole evaporate, and can reconstruct from what he sees that the object fell into the hole before it evaporated.

It is worth to note that this is speculation. What is established science is semiclassical gravity. This is an approximation, where the gravitational field simply follows classical equations, and as the energy-momentum tensor of matter a classical approximation is used. One can be quite sure that this approximation becomes invalid if Planck size effects become relevant because in this case quantum effects have to be taken into account for the gravitational field too.

Now, let's note one aspect where Planck size effects become relevant during the collapse: it is when the collapsing star has reached a size $r_{Schwarzschild} + \varepsilon l_{Planck}$ so that surface time dilation reaches a level where a single Planck time on the surface lasts longer than the age of the universe, or where a particle of Hawking temperature for the outside observer reaches Planck mass energy on the surface.

Saying something about the collapsing star after this size has been reached is pure speculation about a completely unknown theory, quantum gravity. Note that this state will be reached very fast, for star-sized black holes the time is of order of seconds.

I can also add a simple speculation of this type. Once quantum gravity becomes relevant, the collapsing star will reach some ground state before horizon formation and remain in this state forever (or until it collides with other matter).

To underscore my point: This sentence is quantum gravity speculation. But every statement contradicting this sentence is also only quantum gravity speculation. Like the following sentence:

No. The imploding matter continues on inward until it reaches zero surface area and forms the singularity.

A common objection to this argument (essentially the only one I'm aware of) is that if one uses the coordinates of the infalling observer, then nothing special happens near the horizon, so that quantum gravity effects cannot become relevant already near the horizon. But this argument presupposes that in quantum gravity the Strong Equivalence Principle remains valid, which is also quantum gravity speculation. Of course, this particular speculation is quite popular, but there is not much one can say in favor of this hypothesis. In particular, if one gives up the equivalence principles, one can easily construct quantum theories of gravity. (See Donoghue for possibilities for quantum gravity as an effective quantum field theory. It is the field-theoretic version in some diff-symmetry breaking gauge. This symmetry breaking allows to get a well-defined field theory with local energy and momentum of the gravitational field by the standard Noether theorem. Then you can use a lattice regularization of this field theory to get a finite quantum theory gravity.) Instead, a quantum theory of gravity where the strong equivalence principle remains valid is yet unknown.

 

[Nugatory]

A Paradox of the black hole is that GR states the stationary observer experiences time dilation, while the inflating observer experiences no time dilation. By the time the infalling observer reaches the event horizon, an infinite amount of time passes for the other frame of reference. But black holes evaporate in a finite amount of time.. so do physical laws prevent anything from really reaching the event horizon?

That question cannot be answered until you have a clear understanding of what happens when an object is dropped into a black hole when we don’t consider the possibility of evaporation - and it turns out that we have thread on that subject going right now: https://www.physicsforums.com/threads/can-you-even-fall-into-a-black-hole.992212/ (and also many many older threads that a forum search will find).

The quick summary is that no physical laws prevent anything from reaching the horizon, and in fact something dropped into a black hole will pass through the horizon and reach the central singularity within a very short time,

 

[PeterDonis]

What is established science is semiclassical gravity. This is an approximation, where the gravitational field simply follows classical equations, and as the energy-momentum tensor of matter a classical approximation is used.

To be more precise, "semiclassical" means you use the classical EFE for the spacetime geometry, with the expectation value of some appropriate operator as the effective stress-energy tensor.

let's note one aspect where Planck size effects become relevant during the collapse: it is when the collapsing star has reached a size so that surface time dilation reaches a level where a single Planck time on the surface lasts longer than the age of the universe, or where a particle of Hawking temperature for the outside observer reaches Planck mass energy on the surface.

No, this does not make Planck size effects relevant during the collapse, because the "time dilation" you refer to is for a stationary object, i.e., one that is "hovering" at a constant $r$. But the collapsing matter is not stationary; it's free-falling inward.

The proper criterion, according to classical GR, for when quantum gravity effects should become relevant is when the spacetime curvature approaches the Planck scale. That is not even close to being true at, or well inside, the horizon of any black hole of stellar mass or larger.

every statement contradicting this sentence is also only quantum gravity speculation. Like the following sentence

That sentence is simply classical GR, which is what we are using in this forum. Classical GR is a very well confirmed theory, and it gives a clear criterion, given above, for when its predictions should become inaccurate due to quantum gravity effects. So calling those predictions "speculations" is not correct.

if one uses the coordinates of the infalling observer, then nothing special happens near the horizon, so that quantum gravity effects cannot become relevant already near the horizon

The argument has nothing to do with coordinates. It has to do with the spacetime curvature being way, way short of the Planck scale, as stated above. That is an invariant criterion, independent of any choice of coordinates.

this argument presupposes that in quantum gravity the Strong Equivalence Principle remains valid

As noted above, quantum gravity discussions are off topic for this forum. If you want to discuss these kinds of speculations, please start a separate thread in the appropriate forum.

 

[Elias1960]

As noted above, quantum gravity discussions are off topic for this forum. If you want to discuss these kinds of speculations, please start a separate thread in the appropriate forum.

Sorry, but I wrote an answer to a post where something was written about a "spacetime geometry in which the hole can evaporate", and evaporation of BHs is certainly a trans-Planckian effect, thus, a hypothesis about quantum gravity.

No, this does not make Planck size effects relevant during the collapse, because the "time dilation" you refer to is for a stationary object, i.e., one that is "hovering" at a constant r. But the collapsing matter is not stationary; it's free-falling inward. The proper criterion, according to classical GR, for when quantum gravity effects should become relevant is when the spacetime curvature approaches the Planck scale.

Where quantum gravity effects become relevant is something we can tell if we consider particular examples of theories of quantum gravity. The curvature criterion identifies places where one necessarily has to use quantum gravity. But it does not follow at all that everywhere else semiclassical gravity is sufficient. In the approach which I favor quantum gravity would become relevant before horizon formation. So that the claim that quantum gravity becomes relevant only for large curvature is quantum gravity speculation too.

Here I have added some context from older posts:

This sentence is quantum gravity speculation. But every statement contradicting this sentence is also only quantum gravity speculation. Like the following sentence:

When black holes are created by implosion, does GR state the matter inside of the event horizon stays frozen at the time of implosion in time until the end of the black hole's lifespan?

No. The imploding matter continues on inward until it reaches zero surface area and forms the singularity

That sentence is simply classical GR, which is what we are using in this forum. Classical GR is a very well confirmed theory, and it gives a clear criterion, given above, for when its predictions should become inaccurate due to quantum gravity effects. So calling those predictions "speculations" is not correct.

Given the context of the quote, which talked about "black hole's lifespan", thus, making speculative trans-Planckian hypotheses about Hawking radiation lasting until evaporation of the whole BH, answering with a fully classical GR statement would have been very wrong. So I have interpreted it as a statement about what remains valid from classical theory in the trans-Planckian speculation.

 

[PeterDonis]

I wrote an answer to a post where something was written about a "spacetime geometry in which the hole can evaporate"

And there are classical GR models of such a process, the simplest being the outgoing Vaidya metric. Those are the models being discussed in this thread.

evaporation of BHs is certainly a trans-Planckian effect

It might turn out to be when we have a good theory of quantum gravity that has experimental confirmation, but we don't have that now.

 

[PeterDonis]

The OP question has been answered as well as it can be in the context of classical GR, so this thread is closed. Further discussion of how quantum gravity might handle a scenario like that described in the OP should be done in a new thread in the appropriate forum.