# Schwarzschild metric and BH mass

1. Aug 17, 2004

### kurious

What evidence is there that the schwarzschild metric is valid inside a black hole (as opposed to outside the Sun where evidence comes in the form of mercury's perihelion)?
Also, if a black hole is made from photons, would it be massless and move at
the speed of light?

2. Aug 17, 2004

### DW

Are you proposing an alternative?
No.

3. Aug 17, 2004

### marlon

I think this is an unvalid question, kurious? The concept of the Schwarzschildradius comes from the use of the schwardzschild metric. It is just a boundary that indicates the infinite-red-translation of the spectra. I am sure you know the story with the speeds exceeding the lightspeed.

A black hole made of fotons ?????

regards
marlon

4. Aug 17, 2004

### pervect

Staff Emeritus
The Scwarazschild metric *probably* isn't a stable solution for the metric inside a black hole - I posted more details on this somewhere, it's from Kip Thorne's popular book. The metric inside a BH is, according to Thorne, most likely something called a BKL singularity.

However, there is just a wee bit of a problem testing this theoretical prediction. There's an even bigger problem reporting the results back :-)

As for your second question, as I recall, two parallel light beams do not attract each other when moving in the same direction. It's possible to form a black hole out of only light, but it requires that the light not all be travelling in the same direction. This results in a black hole that moves at less than 'c'.

5. Aug 18, 2004

### marlon

Interesting, how can a black hole be formed by using only light ???

regards
marlon

6. Aug 18, 2004

### kurious

Higgs theory says an object either has mass or is massless.
A black hole made from photons would be indistinguishable from one made from rest masses with the same energy.Is a black hole made from photons massless or does it have mass?

7. Aug 18, 2004

### pmb_phy

There is no evidence of this. Nobody has ever been inside a event horizon to tell us if its correct. And if he was there then we'd have to be inside the event horizon too. While we might find out the answer, we'd pay for it with our lives. Frankly, I, personally am not that anxious to find out.
Interesting question. If there were a system of photons which had a zero total momentum then it would be possible for a black hole to form. All that is required is that the photons be located within the black hole. Since the photons have mass then its possible for a black hole to form. This mass would then be the M in the Schwarzschild metric. But this M would be the E/c2 as measured in the zero momentum frame. Some people like to call that "rest mass".

However, if all the photons were moving in the same direction, then a black hole can't form, even if all the mass of the photons is within the "Schwazchild radius" associated with the total mass of the photons. This is easy to see since if all the photons are moving in the same direction there is no zero momentum frame of reference. If a black hole formed then there would be. A person in that frame would then measure a violation of the conservation of momentum. However you'd have to ask yourself how such a beam of photons could be created in the first place. If the matter from which the photons were emitted fit within Rs to begin with then it would seem to me that it was a black hole to begin with (with photons moving in the opposite direction?) and therefore one can't create such a beam.

Pete

Last edited: Aug 18, 2004
8. Aug 18, 2004

### kurious

If a large number of pions decay into photon pairs which travel in
opposite directions, and one member of each pair travels to a fixed
point in space,
a black hole would form at the fixed point in space.Since the photon
polarizations are coupled, I could get information about the
microstates in the black hole by measuring the polarization angles of
the photons that are outside the black hole.
And by placing a number of polarizing filters in a line, for each
photon travelling outside the black hole, with one photomultiplier per
photon to detect each photon, I could gain information on the
microstates in the black hole at different periods in time.So I would
know more about a black hole than just its total spin,mass and
charge.Any objections to this?

9. Aug 18, 2004

### pmb_phy

At what fixed point in space? Why would a black hole form?
You're speaking of commuinication faster than light using entangled states. There is some controversy about whether this is possible or not. People claim to have done it in fact. But I've seen this discussed in the physics literature. I have no opinion on this otherwise since I haven't studied it in detail.

However, as you've described it, this wouldn't seem to work. All you'll get is a random sequence of polarization states and you'd have no way to interpret them.

There was an article in Scientific American back in 1993 called Faster than Light? which "discusses experiments in quantum optics which they claim shows that two distant events can influence each other faster than any signal could have traveled between them."

Note: I've collected a few articles from the physics literature on FTL communication. If anyone is interested in this topic and would like the references than I can post them. They're from journals such as The American Journal of Physics and Annals of Physics etc. I'm just too lazy to post them otherwise.

Pete

Last edited: Aug 18, 2004
10. Aug 18, 2004

### da_willem

The Schwarzschild metric is an exterior solution and is derived as such. So when the empty spacetime field equation holds theoretically the Schwarzschild metric is valid. When the radius of an object is smaller than 2GM/c^2 there is a point where the Schwarzschild line element diverges ($$g_{11}=-(1-2GM/rc^2)^{-1}$$). So I guess all bets are off then. In terms of e.g. Eddington-Finkelstein coordinates you can still investigate what happens inside the black hole using the Schwarzschild metric and it predicts (not unreasonable) ingoing null geodesics. But it's more a matter of faith than science because no experiment could be performed to investigate the validity of the Schwarzschild metric inside a black hole.

11. Aug 18, 2004

Staff Emeritus
AFAIK the black hole is a prediction of the metric, and of theories of stellar collapse. As far as experiment goes, we have never seen an absolute guaranteed black hole. We have inferred that there are black holes at the center of the galaxies but we cannot see them, we only see the violent physics we interpret as coming from a hidden black hole. So the answer to your question is none, just like Hawking radiation and the Beckenstein entropy, and so forth; it's all theory.

12. Aug 18, 2004

### marlon

A blach hole must have restmass. two fotons can generate restmass so I think (it is my opinion though) that a blach hole made of fotons can never be massless or move at the speed of light.

Isn't it the restmass only that curves spacetime???

regards
marlon

13. Aug 18, 2004

### DW

Its not restmass, its just mass. Restmass is a bad word. And, it is the stress-energy tensor that acts as the source term in Einstein's field equations.

14. Aug 18, 2004

### marlon

ok,ok,ok,gues, i stand corrected

regards
marlon

15. Aug 18, 2004

### marlon

So just to get the record straight : it is relativistic mass that curves spacetime, right???

But i have some difficulties accepting the concept of a black hole moving at the speed of light. This is relative. Suppose we can "attach" an observer to the black hole. In his eyes the black hole doesn't move so if it cannot be constructed out of fotons.

Besides, following the QED-feynmann-graphs. Interactions between the fotons (let's say two to make it easy) could occur, generating fermionic-matter-particles like electrons and positrons. The fotons wouldn't last though.

regards
marlon

16. Aug 18, 2004

### pmb_phy

Yes. Misner, Thorne and Wheeler call it mass-energy, or sometimes they call it just "mass", as Wald does at times (at least one place in his text that I know of) but its all the same thing. So long as you pay close attention to how I described it above.
I don't recall ever saying that a black hole could move at the speed of light.

Pete

17. Aug 18, 2004

### kurious

If a black hole consists of photons how could the photons survive given that
they must reach the singularity and stop moving?This violates relativity theory
which says a photon cannot be at rest!
And how could fermions which obey fermi-dirac statistics all be present at the singularity? This would be at odds with quantum mechanics!
Black holes are bad news for quantum mechanics and relativity.The fact that they
are bad news for relativity and that relativity theory describes them suggests an internal inconsistency in relativity theory.

18. Aug 18, 2004

### chroot

Staff Emeritus
kurious:

You are correct. Quantum mechanics and general relativity are at odds with each other. One location where they are not compatible is the "singularity" at the center of a black hole.

In all likelihood, there is no actual singularity at the center of a black hole, just a very dense state of matter. Quantum mechanics prohibits singularities for many reasons. M-theory or another GUT will answer these questions.

- Warren

19. Aug 18, 2004

### zefram_c

This might be relevant... no time to check now. No idea what they could be made of, but remember that GR is a classical theory.

20. Aug 18, 2004

### pervect

Staff Emeritus
Right, modulo the question of wheter or not "relativistic mass" should be called by it's more modern name, "energy".

Not a problem, since black holes don't move at the speed of light.

21. Aug 18, 2004

### pmb_phy

Relativistic mass is not another name for energy. Proportionality of two physical quantities does not mean that the two physical quantities have the same physical meaning. They are defined differently. In fact in relativistic electrodynanics, the term energy is used to describe the sum E = Kinetic Energy + Rest Energy + Potential energy = K + E0 + V = mc2 + V. The quantity T = mc2 is inertial energy and the quantity E is "energy" or "total energy". It would be a mistake to confuse E with T. E is proportional to the time component of the generalized 4-momentum while T is proportional to the regular 4-momentum.

Consider also the relationship energy of a photon and its frequency, i.e. E = hf. Since f is proportional to E would you say that frequency is another name for electromagnetic energy? I know I wouldn't.

Pete

Last edited: Aug 18, 2004
22. Aug 18, 2004

### pervect

Staff Emeritus
It's not just proportionality, it's identity. But I don't think there's much point in arguing the semantics. I refer interested readers to

http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html [Broken]

for why I like to avoid the term "relativistic mass".

A fuller answer to "what curves spacetime" would be "the stress energy tensor" rather than just "energy", of course.

Last edited by a moderator: May 1, 2017
23. Aug 18, 2004

### Haelfix

The question of whether a conglomeration of photons can form a blackhole is rather interesting actually, though its vanishingly small even if the background was a vacuum.

In the real world, regular matter and interactions will swamp the source terms making any second order gravitational QFT interactions (with newtonian coupling constants) tiny and negligable.

Now that I think about it, its darn near impossible, b/c we don't live in a vacuum, and thermodynamics will introduce strong cutoff terms in the QFT lagrangians. Not to mention that its unclear to me at least, how a many body problem like that would work out statistically. Clearly you cant just treat it as a classical thermal bath of photons.

24. Aug 18, 2004

### Orion1

Metric Measurement...

Although the Schwarzschild Metric is a solution in General Relativity, 'static' Schwarzschild BHs with zero angular momentum $$L = 0$$, and based upon the violent nature of their improbable formation, cannot exist in the known Universe. The Schwarzschild Metric is a mathematical solution only, not a real solution in the real Universe.

Schwarzschild BHs do not exist.

25. Aug 18, 2004

### DW

No. There is no place for relativistic mass in modern relativity. It is the stress-energy tensor that is the source term in Einstein's field equation.