"Black holes can only get bigger" - huh?

[PeterDonis]

Using an admittedly simplified form of the Friedmann equation

Which is the wrong one to use for the case you are analyzing (dark energy dominated). The correct Friedmann equation is

$$
\frac{1}{a} \frac{da}{dt} = H_0
$$

This gives the following equation for $t$:

$$
t = \frac{1}{H_0} \ln a
$$

Since the log of the $a$ you calculated is about $50$ (natural log, not log to the base 10), this gives $t \approx 7 \times 10^{11}$ years.

 

[Buzz Bloom]

The correct Friedmann equation is

Thank you Peter. At my advanced years I sometimes make very silly careless errors when I know better.

 

[Buzz Bloom]

we have no way of experimentally testing for Hawking radiation now or in the foreseeable future.

Assuming Hawking radiation is a real phenomenon, a while ago I made a calculation that it is extremely difficult to setup a suitable radio telescope near a BH which can detect the very low Hawking radiation temperature while avoiding the much higher temperature of interfering CMB radiation. Based on this result I concluded that intelligent beings will never exist at a distant future time time when the BH Hawking radiation temperature might be near the CMB temperature and actually be detectable.

 

[PeterDonis]

it is extremely difficult to setup a suitable radio telescope near a BH which can detect the very low Hawking radiation temperature while avoiding the much higher temperature of interfering CMB radiation.

It actually might still be possible to pick the Hawking radiation out of the CMB background because of its different distribution by direction. Basically you would look for a "bump" in the CMB (a higher amplitude than the CMB black-body distribution) at a particular frequency that was only present in the direction of the BH. At the frequency where we would expect the BH Hawking radiation to peak, the CMB amplitude would be much lower than at the CMB peak (which is what just looking at the CMB temperature would give you), so the BH peak might still be detectable.

Based on this result I concluded that intelligent beings will never exist at a distant future time time when the BH Hawking radiation temperature might be near the CMB temperature and actually be detectable.

I'm not sure why you would conclude this. Even if it turns out not to be possible to build the required radio telescope, that doesn't mean intelligent beings can't exist at that time. They just wouldn't be able to build the telescope.

 

[Buzz Bloom]

that doesn't mean intelligent beings can't exist at that time.

My calculation (possibly flawed) is that the future time when the Hawking radiation temperature equals the CMB temperature, taking into account that today's BH's will get much bigger (due to merging) with much lower temperatures, that the environment in the Milky Way will have reached a state that will not support life. On the other hand, maybe robotic intelligence might still survive then, but my pessimistic view rejects this possibility.

 

[PeterDonis]

My calculation (possibly flawed) is that the future time when the Hawking radiation temperature equals the CMB temperature, taking into account that today's BH's will get much bigger (due to merging) with much lower temperatures, that the environment in the Milky Way will have reached a state that will not support life.

Whether such a calculation is right or wrong, it has nothing whatever to do with whether or not a radio telescope can be built that can detect Hawking radiation from a BH. Your previous post made it appear that you were claiming a connection between those two things; that's what I was questioning.

 

[Sunil]

I am wondering about the division of opinions on this topic. Can you make a rough estimate of the fraction of physicists who have each of one of three logically possible opinions?
1. Hawking radiation is definitely more likely than not to be a real possible phenomenon.
2. Hawking radiation is definitely more likely than not to not be a real possible phenomenon.
3. It is more-or-less equally likely that Hawking radiation is or is not a real possible phenomenon.

I have no data about the opinions, but it looks like a majority has never heard about the trans-Planckian problem of the derivation at all and so they think Hawking's derivation is fine, thus, Hawking radiation is a certain prediction of semiclassical gravity.

There have been many attempts to find variants of the proof which do not rely on trans-Planckian assumptions. They all failed, and it is quite easy to identify the weak points. One has to know that stable stars don't radiate Hawking radiation - you obtain it only if there is a change of the gravitational field which also leads to a change of the vacuum state. Without change of the vacuum state no radiation. Then, it is sufficient to recognize that one can modify GR in the trans-Planckian domain in such a way that the collapse stops. All you need is a force against the collapse which becomes greater if time dilation (in preferred Schwarzschild-like coordinates - a modified GR can have them) becomes astronomical so that $10^{-100}$ Planck time on the surface means more than $10^{100}$ times the age of the universe for the far away observer. If in that modification the collapse stops, there will be no Hawking radiation (except during collapse time). See arxiv:0906.1768 for how fast it stops (almost immediately).

Nonetheless, who cares, once there are many many different "proofs"?

The most impressive arguments for those who are at least aware of the trans-Planckian problem are analogies. Surprisingly many accept the analogy with Unruh radiation: Acceleration leads to some similar radiation effect. Surprisingly, because it can be easily shown to be false: Stable stars don't Hawking-radiate despite the fact that they give some acceleration.

The other analogy argument which has been quite powerful (in its sociological influence, not in its argumentative strength) are "dumb holes" in condensed matter theory. The point is that they seem to circumvent the trans-Planckian problem because they have an explicit cutoff - atomic distances. Nonetheless one can show some Hawking-like radiation. What if we confront this analogy (as suggested above) with some stable configuration? We will see that all the examples of "dumb holes" have nontrivial flows, thus, even if as flows they are stable, on the atomic level they are not stable - the atoms move.

To summarize, I would not suggest to care about majority positions in physics, simply because the majority does not take care about the details. This holds in physics as well as in politics - following the majority may be a reasonable political decision if one wants to optimize the own interest, but it is not a good idea if one wants to find out the truth.

 

[martinbn]

I have no data about the opinions, but it looks like a majority has never heard about the trans-Planckian problem of the derivation at all and so they think Hawking's derivation is fine, thus, Hawking radiation is a certain prediction of semiclassical gravity.

Can you give some references? The one you gave above doesn't seem to talk about the trans-Plackian problem.

 

[Vanadium 50]

My calculation

Calculations involve numbers. I don't think you have enough to do what you claim.

 

[stevendaryl]

The discussion about Hawking radiation makes me want to spend some time (it will probably take me years, so I better get started) understanding Hawking radiation and Unruh radiation.

I'm wondering about the analogy between the two. Are they analogous enough that the absence of Hawking radiation would count as a violation of the equivalence principle?

 

[PeterDonis]

it is sufficient to recognize that one can modify GR in the trans-Planckian domain in such a way that the collapse stops.

That's not what the paper you referenced shows. That paper simply assumes that it is possible to have a trajectory for an ingoing shell in which the shell asymptotically approaches some areal radius $R$ which is a little bit larger than $2M$, and computes what outgoing radiation visible at infinity would be present in such a case assuming a scalar quantum field and s-wave emission only. It does not show any "modification" of GR, whether in the trans-Planckian domain or not, that implies such a trajectory; in fact, it does not appear to claim that GR needs any modification at all.

 

[PeterDonis]

Acceleration leads to some similar radiation effect. Surprisingly, because it can be easily shown to be false: Stable stars don't Hawking-radiate despite the fact that they give some acceleration.

You are mis-stating the analogy. Unruh radiation is an easily derived property of a quantum field in flat spacetime in the presence of an accelerated observer; it associates the radiation with the presence of a Rindler horizon for such an observer. The analogy with Hawking radiation relies on the fact that, for an accelerated observer close enough to the event horizon of a black hole, the hole's event horizon is the same as the observer's Rindler horizon. But that only holds for a black hole (and for an observer accelerating to "hover" close enough to the hole's horizon); it does not hold for an ordinary star, since the star is not a black hole and has no event horizon.

 

[PeterDonis]

If in that modification the collapse stops, there will be no Hawking radiation (except during collapse time).

At the bottom of p. 3, the paper says that this possibility is unlikely:

"These results strongly suggest that the conventional wisdom as regards the formation of black hole is correct and that the semiclassical radiation does not prevent the formation of the event horizon."

 

[Sunil]

Can you give some references? The one you gave above doesn't seem to talk about the trans-Plackian problem.

Unruh, W. G. (1981). Experimental Black-Hole Evaporation, Physical Review Letters 46(21), 1351-1353 is the paper where the dumb holes are introduced.

This is a nice review about the trans-Planckian problem:
Helfer, A.D. (2003). Do black holes radiate? Rept. Prog. Phys. 66, 943-1008, arxiv:gr-qc/0304042
It concludes:

None of the derivations that have been given of the prediction of radiation from
black holes is convincing. All involve, at some point, speculations of what physics is like
at scales which are not merely orders of magnitude beyond any that have so far been
investigated experimentally ($\sim 10^3$ GeV), but at and increasing beyond the Planck
scale ($\sim 10^{19}$ GeV), where essentially quantum–gravitational effects are expected to
be dominant. (In Hawking’s treatment, this increase occurs exponentially quickly.)
Some of these speculations may be plausible, but none can be considered reliable.

 

[Buzz Bloom]

Calculations involve numbers. I don't think you have enough to do what you claim.

Hi Vanadium:

I apologize for the unintentional ambiguity of "my calculation". I was referring to a calculation I made several years ago about the rate of loss mass of a BH starting at today's time due to Hawking radiation, and how long it would take before the BH had loss sufficient mass for its temperature to become larger while the CMB temperature became smaller until they were equal. I have lost that calculation, as well as some of the components I used then, so I can at this time no longer recreate this calculation. I also did not at that time include the increase on a BH's mass due to merging with other mass, but I believe that it is possible for a suitably trained person (not me) to do this.

I also calculated some years ago the time it would take for Earth to fall into the sun due to losses in orbital energy due to the orbit produced Gravitational waves. That calculation has also become lost.

Recently, in another thread,

https://www.physicsforums.com/threads/collapsing-orbit-due-to-gravitational-wave.1004330​

post #7​

@pervect provided the math sufficient for reproducing the Earth-sun calculation, as well as some clarity that a much more complex math process is needed to make a similar calculation about two BHs. This means that the math to calculate an approximation for the time it would take for all the baryon mass in the Milky Way to merge into a single BH is much too complicated for an amateur like myself to do.

Regards,
Buzz

 

[PeterDonis]

It concludes

Note that this conclusion does not mean Hawking radiation definitely does not happen, or should no longer be considered as a possible prediction. It means we don't really know either way. As the same paper says in its abstract:

"[A] definitive theoretical treatment will require an understanding of quantum gravity in at least some regimes. Until then, no compelling theoretical case for or against radiation by black holes is likely to be made."

 

[Sunil]

That's not what the paper you referenced shows. That paper simply assumes that it is possible to have a trajectory for an ingoing shell in which the shell asymptotically approaches some areal radius $R$ which is a little bit larger than $2M$, and computes what outgoing radiation visible at infinity would be present in such a case assuming a scalar quantum field and s-wave emission only. It does not show any "modification" of GR, whether in the trans-Planckian domain or not, that implies such a trajectory; in fact, it does not appear to claim that GR needs any modification at all.

That's why I added "for the mathematics". I should have written "for the mathematics of how fast the Hawking radiation stops if the collapse stops".

At the bottom of p. 3, the paper says that this possibility is unlikely:

"These results strongly suggest that the conventional wisdom as regards the formation of black hole is correct and that the semiclassical radiation does not prevent the formation of the event horizon."

I have not claimed that in semiclassical GR semiclassical radiation prevents the formation of the event horizon. A paper which makes such a claim is

Gerlach, U.H. (1976). The mechanism of blackbody radiation from an incipient black hole, Phys Rev D 14(6) 1479-1508.

I'm neutral about this question. My point is simply that QG is unknown, that we can have QG effects if the surface time dilation reaches factors like $10^{100} t_{age-of-universe}/t_{Planck}$, and if we assume that unknown QG effects stop the collapse once such a factor is reached, then we can used the Paranjape paper to see that there will be no Hawking radiation. (If we think that this needs more justification than simply "stable stars don't radiate".) For this sufficiently simple argument I have no reference in the literature.

You are mis-stating the analogy. Unruh radiation is an easily derived property of a quantum field in flat spacetime in the presence of an accelerated observer; it associates the radiation with the presence of a Rindler horizon for such an observer. The analogy with Hawking radiation relies on the fact that, for an accelerated observer close enough to the event horizon of a black hole, the hole's event horizon is the same as the observer's Rindler horizon. But that only holds for a black hole (and for an observer accelerating to "hover" close enough to the hole's horizon); it does not hold for an ordinary star, since the star is not a black hole and has no event horizon.

Whatever, it does not work. What can cause radiation has to be inside the backward light cone. There is no event horizon in that backward light cone.

 

[PeterDonis]

If we think that this needs more justification than simply "stable stars don't radiate".

Which, as I have already pointed out, is an invalid argument since the radiation, in the conventional view, is associated with an event horizon, and stable stars have no event horizon.

Whatever, it does not work. What can cause radiation has to be inside the backward light cone. There is no event horizon in that backward light cone.

If this argument is correct, it is an argument that there is no Unruh radiation. Do you have a refutation of Unruh's derivation of Unruh radiation? If you don't, you should consider the possibility that it is your argument here that is wrong, not the derivation of Unruh radiation.

 

[Sunil]

Which, as I have already pointed out, is an invalid argument since the radiation, in the conventional view, is associated with an event horizon, and stable stars have no event horizon.

Not in the context of that argument (I assume that some unknown QG effects stop the collapse when surface time dilation becomes astronomical.)

If this argument is correct, it is an argument that there is no Unruh radiation. Do you have a refutation of Unruh's derivation of Unruh radiation? If you don't, you should consider the possibility that it is your argument here that is wrong, not the derivation of Unruh radiation.

No, Unruh radiation is in Minkowski space, everything is time symmetric. My argument uses the time asymmetry - in the past lightcone, the observer sees the collapsing star before horizon formation. I don't consider eternal BHs and don't think it applies to them.

Note that this conclusion does not mean Hawking radiation definitely does not happen, or should no longer be considered as a possible prediction. It means we don't really know either way. As the same paper says in its abstract:

"[A] definitive theoretical treatment will require an understanding of quantum gravity in at least some regimes. Until then, no compelling theoretical case for or against radiation by black holes is likely to be made."

Correct. AFAIK nobody claims that it is an impossible prediction.

 

[PeterDonis]

Not in the context of that argument (I assume that some unknown QG effects stop the collapse when surface time dilation becomes astronomical.)

Such an object would not be a "stable star" since it is impossible for such an object to be made of stress-energy that obeys energy conditions (which all ordinary matter and radiation does), because of the Buchdahl Theorem: an object made of ordinary matter can only be stable if its radius is greater than 9/8 the Schwarzschild radius for its mass.

It is known that quantum fields can have an effective stress-energy tensor that violates energy conditions; however, the usual effect of such violations is instability: objects either collapse or explode. So the most natural assumption of the "unknown effects" you assume to be present is not that a collapse would just stop at some radius slightly larger than the Schwarzschild radius, and form a stable object of that radius made of exotic matter (i.e., "quantum stuff" that violates energy conditions). The most natural assumption is that the collapse would turn into an explosion, as in the various quantum "bounce"models.

 

[PeterDonis]

Unruh radiation is in Minkowski space

As the background spacetime, yes. But the background spacetime is not all that is present. See below.

everything is time symmetric.

Wrong. The process of detecting Unruh radiation is not time symmetric: a particle detector carried by the accelerated observer can be taken from its ground state to an excited state by interacting with the quantum field; the observer interprets this as "detection of a particle". The quantum field undergoes a corresponding transition. This is a time asymmetric process.

Another way of seeing the time asymmetry is as follows: the Unruh radiation is coming out of the Rindler horizon, but there is no radiation going in to the Rindler horizon (because the quantum field state is the vacuum state with respect to inertial observers, and that state contains no radiation coming in from past infinity). This is a time asymmetric condition.

 

[Sunil]

As the background spacetime, yes. But the background spacetime is not all that is present.

Ok, my "everytyhing" was sloppy, sorry.

Such an object would not be a "stable star" since it is impossible for such an object to be made of stress-energy that obeys energy conditions (which all ordinary matter and radiation does), because of the Buchdahl Theorem: an object made of ordinary matter can only be stable if its radius is greater than 9/8 the Schwarzschild radius for its mass.

It would not be a stable star in classical GR. So what? As I said, I presuppose that unknown QG effects stop the collapse.

The most natural assumption is that the collapse would turn into an explosion, as in the various quantum "bounce"models.

It is not my intention to speculate about the QG details. But my intuition tells me that there will be not that much difference between an atom and a BH - they both will have a stable ground state.

 

[PeterDonis]

my intuition tells me

"Intuition" is not what we're supposed to be basing discussion on. We understand what your opinion is, but your opinion is not the same as established fact, nor is it a valid reference.

 

[Sunil]

"Intuition" is not what we're supposed to be basing discussion on. We understand what your opinion is, but your opinion is not the same as established fact, nor is it a valid reference.

No problem - I have simply answered a claim about a "most natural assumption ... that the collapse would turn into an explosion" by giving another assumption. Is is obvious that speculations about unknown quantum gravity effects cannot be established facts and cannot be supported by valid references. The best one can support it is by some vague analogies, which I have done, with the reference to the ground state as the most important quantum effect for atoms.

 

[Fra]

Is is obvious that speculations about unknown quantum gravity effects cannot be established facts and cannot be supported by valid references. The best one can support it is by some vague analogies, which I have done, with the reference to the ground state as the most important quantum effect for atoms.

I am guessing that what Peter means is that in these the rules suggest that only "published speculations" should be discussed? not becase they are necessarily right but because it at least prevents random personal and pedestrian speculations from degrading forum quality.

But I agree this sometimes makes the discussions "difficult" or constrained, from a creative perspective or idea exchange perspective, I have no personal issues with speculation as long as its reasonble and not complete random layman speculation. I think the moderators are doing a good job still here to keep the forum sane.

Maybe the thread would have been better in BTSM or QM foundations? How can one talk about GR+QM without touching upon QM foundations? This was what I meant with post 17 as well.

/Fredrik

 

[Sunil]

I am guessing that what Peter means is that in these the rules suggest that only "published speculations" should be discussed? not becase they are necessarily right but because it at least prevents random personal and pedestrian speculations from degrading forum quality.

I take care about my posts not degrading a particular thread, especially if mods are involved. Peter has not given a reference to his speculation, and in such situations I conclude this is fine in this context.

 

[PeterDonis]

I am guessing that what Peter means is that in these the rules suggest that only "published speculations" should be discussed?

And even that only in the Beyond the Standard Model forum. Which this isn't.

Granted, any quantum discussion of black holes is kind of borderline here, since we don't have an established theory of quantum gravity. But for purposes of this thread, we are discussing the closest thing to a "standard" model of black hole evaporation, the model originally proposed by Hawking. It's good to be aware that there are issues that have been raised with this model and that there are other proposed models, but if we really want to get into a detailed discussion of those issues we probably need to start a separate thread in the BTSM forum.

not becase they are necessarily right but because it at least prevents random personal and pedestrian speculations from degrading forum quality.

Maintaining the signal to noise ratio of PF is one reason, yes. There are at least two others: first, PF is not a platform for conducting original research, and personal speculations/theories that aren't in the published literature are original research; and second, the published literature at least provides a common basis for discussion.