Black Hole - Conservation of energy?

[jnorman]

since energy absorbed by a BH is no longer available to the universe, why is that not a violation of the principle of conservation of energy?

 

[ModusPwnd]

Conservation of energy means that the amount of energy contained in a closed system is constant. It makes no claim as to whether the energy is "available" or not.

 

[mfb]

In addition, there is no global energy conservation in General Relativity. If you consider the total energy content of "black hole + stuff you throw in" in an appropriate way, it will stay constant (the black hole grows and increases its mass), but you cannot simply use energy conservation everywhere.

 

[mathman]

The conservation law applies to the total of mass plus energy. This total includes the dark energy. The dark energy density (according to current theory) is constant as a function of time. Since the universe is expanding, the total energy in the universe is increasing, rather than constant.

 

[Crazymechanic]

@mathman you said the total energy in the universe is increasing , how can that be as energy/mass can't just come from "thin air" ? Where is that energy then coming from in a universe that already has some amount of energy let's say "X"

 

[PeterDonis]

since energy absorbed by a BH is no longer available to the universe

This is incorrect; the energy is still there, contained in the mass of the hole. Any time a BH absorbs energy, its mass increases.

 

[bcrowell]

There is no conservation law for a scalar mass-energy in GR that applies globally in all spacetimes. However, there are measures of mass such as the Komar mass that apply in special cases. The Komar mass is defined and conserved in asymptotically flat spacetimes. If you have a black hole in an asymptotically flat spacetime and drop some mass into it, the total Komar mass is conserved. As PeterDonis pointed out, conservation of mass-energy doesn't have anything to do with whether the mass-energy is "available."

The conservation law applies to the total of mass plus energy. This total includes the dark energy. The dark energy density (according to current theory) is constant as a function of time. Since the universe is expanding, the total energy in the universe is increasing, rather than constant.

It's not increasing, just undefined. We have a FAQ about this: https://www.physicsforums.com/showthread.php?t=506985

 

[PAllen]

There is no conservation law for a scalar mass-energy in GR that applies globally in all spacetimes. However, there are measures of mass such as the Komar mass that apply in special cases. The Komar mass is defined and conserved in asymptotically flat spacetimes. If you have a black hole in an asymptotically flat spacetime and drop some mass into it, the total Komar mass is conserved. As PeterDonis pointed out, conservation of mass-energy doesn't have anything to do with whether the mass-energy is "available."

Are you sure you mean Komar mass? That is only defined for stationary spacetimes, which technically cannot accommodate matter falling into a black hole. What is conserved in an asymptotically flat spacetime is ADM mass.

 

[mathman]

It's not increasing, just undefined. We have a FAQ about this: https://www.physicsforums.com/showthread.php?t=506985

My understanding of this subject was based on the fact that in the early universe the expansion was slowing down. However as the the universe expanded the effect of dark energy increased so that it is now speeding up. Another fact (according to my understanding) is that the percentage of total energy in the universe due to dark enenrgy is increasing (universe expansion and constant energy density). All this information is second hand - I am not a physicist.

 

[bcrowell]

Are you sure you mean Komar mass? That is only defined for stationary spacetimes, which technically cannot accommodate matter falling into a black hole. What is conserved in an asymptotically flat spacetime is ADM mass.

Oops, you're right. Thanks for the correction.

 

[Naty1]

since energy absorbed by a BH is no longer available to the universe, why is that not a violation of the principle of conservation of energy?

How about:

A static observer hovering outside the horizon supposedly sees a huge amount of energy from the BH horizon...and according to descriptions I have seen gets fried...


What I am unsure about is that apparently the space-times in our models are static...like Schwarzschild... but when actual matter or a detection device with mass hovers space-time actually becomes dynamic... The horizon moves outward...

It is not clear to me how the static space-time[ idealized model] may affect the above description. In other words, strictly, speaking the models only apply to a "test object observer' hovering for all time...

 

[pervect]

As far as I know, the observer outside the event horizon doesn't see any energy, clasically. And non-clasically he just sees Unruh radiation, which he would see if he were accelerating at the same rate as he needed to be accelerating in flat space-time.

I might have gotten the later part slightly wrong, I'm not as familar with the QM aspects as I wish I was - but i think it's close.

There is a place where observers are expected to be fried when falling into relaitic rotating or charged black holes, but that's due to the effect called "mass inflation" and it occurs inside the event horizon. http://casa.colorado.edu/~ajsh/bhtalk_07/inflation.html has a short note, the same author has some more detailed papers.

 

[PeterDonis]

As far as I know, the observer outside the event horizon doesn't see any energy, clasically.

That's my understanding. Classically, the stress-energy tensor is zero, which means all observers see vacuum, i.e., zero energy.

And non-clasically he just sees Unruh radiation, which he would see if he were accelerating at the same rate as he needed to be accelerating in flat space-time.

Technically, I think an observer hovering above a BH horizon sees Hawking radiation, not Unruh radiation; Unruh radiation is what the corresponding observer in flat spacetime sees. However, AFAIK the mathematical derivations of the two are very similar, so I'm not sure they're really supposed to be viewed as "different" phenomena. The key is that the "particle content" of the quantum field is different for inertial observers and accelerated observers.

If we try to look at this "semi-classically", I think what this is saying is that when quantum fields are present, there is no such thing as a true "vacuum" stress-energy tensor; i.e., the SET of a quantum field cannot be identically zero. Components of it can vanish in particular frames, but it can't vanish as a whole.

 

[PAllen]

As far as I know, the observer outside the event horizon doesn't see any energy, clasically. And non-clasically he just sees Unruh radiation, which he would see if he were accelerating at the same rate as he needed to be accelerating in flat space-time.

I might have gotten the later part slightly wrong, I'm not as familar with the QM aspects as I wish I was - but i think it's close.

There is a place where observers are expected to be fried when falling into relaitic rotating or charged black holes, but that's due to the effect called "mass inflation" and it occurs inside the event horizon. http://casa.colorado.edu/~ajsh/bhtalk_07/inflation.html has a short note, the same author has some more detailed papers.

I am guessing Naty1 is referring to the hypothesized 'black hole firewalls' which is a subject of active research/debate. The debate is far from settled, at this point. Since most attention seems garnered by the 'pro' position of Polchinski, I reference a significant 'anti' paper, also by string community (Susskind started anti, then waffled):

http://arxiv.org/abs/1211.6767