# Black Hole - Conservation of energy?

• jnorman
In summary: They would still see Unruh radiation since he is in a static space-time. But the energy from the horizon would not reach him as it would in a dynamic model.
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?

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.

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.

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.

@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"

jnorman said:
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.

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."

mathman said:
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.

bcrowell said:
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.

bcrowell said:

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.

PAllen said:
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.

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?

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...

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.

pervect said:
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.

pervect said:
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.

pervect said:
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

## 1. What is a black hole?

A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. This happens when a massive star collapses under its own gravity.

## 2. How does conservation of energy apply to black holes?

Conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the case of black holes, the energy of a collapsing star is transformed into gravitational potential energy, which is then stored within the black hole.

## 3. Can black holes violate the law of conservation of energy?

No, black holes do not violate the law of conservation of energy. While it may seem that energy is disappearing into the black hole, it is actually being transformed into a different form, as explained by Einstein's theory of general relativity.

## 4. How does Hawking radiation affect the conservation of energy in black holes?

Hawking radiation is a theoretical form of radiation that is believed to be emitted by black holes. This radiation carries away a small amount of energy from the black hole, causing it to slowly lose mass. However, this does not violate the law of conservation of energy as the lost energy is balanced out by the gain in energy of the emitted radiation.

## 5. Is the conservation of energy the only law that applies to black holes?

No, conservation of energy is just one of the many laws of physics that apply to black holes. Other laws, such as conservation of momentum and angular momentum, also play a role in understanding the behavior of black holes.

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