Is the mass of a black hole diminishing for a free falling observer ?

[dreynaud]

It is known since Hawking that an observer "a rest" at some far distance of a black hole sees a thermal radiation emitted by the black hole. The mass of the black hole diminishes while it emmits the thermal flow of particles.
For a free falling observer there is no thermal radiation. So, for him the mass of the black hole may not diminish; it may remains constant.

However, the mass should be a well defined observable for both observers, so that they should agree with their observed value of the mass.

Can someone help to understand this paradox ?

 

[PAllen]

It is known since Hawking that an observer "a rest" at some far distance of a black hole sees a thermal radiation emitted by the black hole. The mass of the black hole diminishes while it emmits the thermal flow of particles.
For a free falling observer there is no thermal radiation. So, for him the mass of the black hole may not diminish; it may remains constant.

However, the mass should be a well defined observable for both observers, so that they should agree with their observed value of the mass.

Can someone help to understand this paradox ?

Mass is not a local observable at all in GR. It has not even been successfully defined as a quasi-local quantity. The best that can be done is definition as a global quantity, and even this is possible only for some boundary conditions (e.g. for asymptotic flatness at infinity).

More to the point, I don't think your claims about free falling observers are justified. See:

http://arxiv.org/abs/1101.4382

which argues that free falling observers from infinity experience intensified Hawking radiation as they cross the horizon.

 

[dreynaud]

Thanks for your answer. I'm going to read the article you cite.
I quickly add somme comments :
- That a free falling observer doesn't experience any thermal radiation is a well based property discussed by Hawking in early 70s articles and Unruh, also explained by Kip Thorne in his book (that I have) on membrane paradygm, and by many other physicits (I may add online references later).

- About the observation of the mass, I was talking about the mass parameter that appears in the schwarzschild metric. This parameters should be observable since it determines the geometry of the space-time. I agree that there is a problem in defining the energy in General Relativity.

 

[PAllen]

Thanks for your answer. I'm going to read the article you cite.
I quickly add somme comments :
- That a free falling observer doesn't experience any thermal radiation is a well based property discussed by Hawking in early 70s articles and Unruh, also explained by Kip Thorne in his book (that I have) on membrane paradygm, and by many other physicits (I may add online references later).

- About the observation of the mass, I was talking about the mass parameter that appears in the schwarzschild metric. This parameters should be observable since it determines the geometry of the space-time. I agree that there is a problem in defining the energy in General Relativity.

The mass parameter of SC geometry is not locally observable. Only global observations can measure it - as feature of the geometry of the manifold as a whole. In the presence of Hawking radiation, you no longer have static geometry, nor a vacuum solution anywhere. Thus, you no longer have exact SC geometry.

 

[dreynaud]

The article you've suggested is very interesting. However I think that the question remains :

The vacuum is first set rlativelty to a "reference observer" such that : "This vacuum state has been fixed by requiring that a reference observer freely falling from innity detects no radiation".
Then the vacuum is studied as seen by a "freely-falling observers from infnity, with different time delays with respect to the reference observer". Particles flux is observed by the second free falling observer.
It seems to be caused by the fact they use the vacuum of the first observer in the context of the second free falling observer. Do you agree ?

However, the question remains for the first free falling observer that never sees radiations. If so, he will never see any final explosion of the black hole, whereas the observer that experiences radiations, will see explosion after a finite laps of time.You wrote : "The mass parameter of SC geometry is not locally observable. Only global observations can measure it". Ok, so it is an observable.

 

[PAllen]

The article you've suggested is very interesting. However I think that the question remains :

The vacuum is first set rlativelty to a "reference observer" such that : "This vacuum state has been fixed by requiring that a reference observer freely falling from innity detects no radiation".
Then the vacuum is studied as seen by a "freely-falling observers from infnity, with different time delays with respect to the reference observer". Particles flux is observed by the second free falling observer.
It seems to be caused by the fact they use the vacuum of the first observer in the context of the second free falling observer. Do you agree ?

However, the question remains for the first free falling observer that never sees radiations. If so, he will never see any final explosion of the black hole, whereas the observer that experiences radiations, will see explosion after a finite laps of time.You wrote : "The mass parameter of SC geometry is not locally observable. Only global observations can measure it". Ok, so it is an observable.

Free falling observers will reach the singularity long before any explosion of the black hole. More generally, this whole field is a 'best attempt' to do quantum physics + GR without and adequate theory. Pressing too hard, and I would expect unresolvable issues.

As for measuring mass, a global observable means it is not measured with respect to any observer at all, only by measuring total geometry, which is coordinate independent. Observers in GR are (take your pick per various experts): (1) a useless carryover from SR that should be abandoned; (2) strictly locally useful (therefore you can't talk about global measurements per 'an observer').

As for your interpretation of the paper, I have not had a chance to read it thoroughly and don't plan to any time soon. I referenced it to dispute the general notion that Hawking radiation for different observers is a 'settled question'. I think it is unsettled, so that drawing deep conclusions from an unsettled interpretation of an adhoc, inconsistent theory (QM + GR), is methodologically suspect.

 

[dreynaud]

Free falling observers will reach the singularity long before any explosion of the black hole. More generally, this whole field is a 'best attempt' to do quantum physics + GR without and adequate theory. Pressing too hard, and I would expect unresolvable issues.

> Yes I agree.

As for measuring mass, a global observable means it is not measured with respect to any observer at all, only by measuring total geometry, which is coordinate independent. Observers in GR are (take your pick per various experts): (1) a useless carryover from SR that should be abandoned; (2) strictly locally useful (therefore you can't talk about global measurements per 'an observer').

> Yes. The point is that the two guys live in the same geometry. GR establishes relation between geometry and material content; so the two guys sould also agree on this content on the basis of GR.

As for your interpretation of the paper, I have not had a chance to read it thoroughly and don't plan to any time soon. I referenced it to dispute the general notion that Hawking radiation for different observers is a 'settled question'. I think it is unsettled, so that drawing deep conclusions from an unsettled interpretation of an adhoc, inconsistent theory (QM + GR), is methodologically suspect.

> I precisely wanted to know if someone had read something on this question, but may be it is still unsloved.

I think we may conclude that the question is still open...

 

[PAllen]

Agree.

Here is another paper arguing the point of view the infalling observers do see Hawking radiation:

http://arxiv.org/abs/0806.0628