Exploring the Energy of Black Holes: A Curious Mind's Guide

[Quarlep]

Hello?
I have a doubt about black holes energy.I am curious about that.What is the Black Holes energy?

Thanks for Help

 

[PeterDonis]

What is the Black Holes energy?

The simple answer is, its mass. If you want more information than that, you will need to clarify your question.

 

[Quarlep]

I thought like you in first but I think its a black hole not a particle.You wanted to say energy equal m c square but it is not a particle it is a black hole isn't it(I know that I said twice)

 

[PeterDonis]

I thought like you in first but I think its a black hole not a particle.You wanted to say energy equal m c square but it is not a particle it is a black hole isn't it(I know that I said twice)

Yes, a black hole is not the same as an ordinary particle. So what? It still has mass, and mass is still equivalent to energy in relativity.

 

[Quarlep]

Then show me an article or mathematical explanation

 

[Quarlep]

And even its true how do you measure it

 

[WannabeNewton]

We can always define the energy of stationary space-times as long as they are asymptotically flat which, in a very loose sense means that the space-time looks more and more like Minkowski space-time the farther out you go from an isolated self-gravitating body. For a Schwarzschild black hole, this energy (called the Komar energy) will exactly equal the Schwarzschild mass of said system, as a very simple calculation shows. However you need to know basic tensor calculus in order to attempt and/or understand the calculation so there's not much we can do there for you unless you already do know the required tensor calculus.

 

[Naty1]

qualep
Here is a quick view:

http://en.wikipedia.org/wiki/Black_hole#Physical_properties

The simplest black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.[8] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.[37] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[38]

If you read the entire article you'll see BH do not emit nor reflect any signals...except gravity and gravitationmal waves...so we cannot see/observe them very easily...They don't reflect light or radar waves for example, so they seem like a 'black hole' if other stuff is not in the way blocking our view. But outside their horizon, their gravitational effects are much like other massive objects so their mass can be calculated based on observed interactions with visible bodies.

Any angular momentum can be measured from far away using frame dragging by the gravitomagnetic field. In the above article, look under HISTORY near the start of the article to see an illustrative example of gravitational lensing.

For some other illustrations and animations see here:
http://en.wikipedia.org/wiki/Supermassive_black_hole

 

[PeterDonis]

Then show me an article or mathematical explanation

An explanation of what? The fact that black holes have mass? Look at any basic GR textbook. That mass is equivalent to energy? Look at any basic SR textbook. The links that Naty1 gave might also help.

And even its true how do you measure it

The same way you measure the mass of any astronomical object. The simplest way is to put something in orbit around it and measure the orbital parameters, then plug into Kepler's Third Law.

 

[Quarlep]

Thanks for your help I thought that their energy will be infinity

 

[Quarlep]

Thanks I got it.I thought wrong.

 

[tom.stoer]

Strictly speaking the energy (energy-momentum tensor) of a Schwarzschild black hole is zero b/c it's a vacuum solution.

 

[Naty1]

Thanks for your help I thought that their energy will be infinity

Nothing has ever been observed nor measured as infinite. That is an experimentally unverified theoretical concept. [But still interesting, as say in the possible extent of the universe.]

 

[Jonathan Scott]

Strictly speaking the energy (energy-momentum tensor) of a Schwarzschild black hole is zero b/c it's a vacuum solution.

That's misleading. The energy-momentum tensor in the vacuum outside the central mass is indeed zero, regardless of whether it is a black hole, as that is part of the vacuum solution, but that does not include the central mass.

The total energy of the central mass is perfectly well-defined, and the shape of space-time in the vacuum outside a static spherical mass only depends on the total energy, regardless of whether it is a black hole.

 

[PeterDonis]

The total energy of the central mass is perfectly well-defined, and the shape of space-time in the vacuum outside a static spherical mass only depends on the total energy, regardless of whether it is a black hole.

This was what I was referring to in my initial response to the OP. I didn't think it was worth getting into the complications involved with talking about the stress-energy tensor, since it seemed like the OP was asking about the total energy of the hole.

 

[WannabeNewton]

Strictly speaking the energy (energy-momentum tensor) of a Schwarzschild black hole is zero b/c it's a vacuum solution.

But the energy-momentum tensor doesn't include gravitational energy density. Even in vacuum we can still define a pseudo-tensor that yields a sufficient notion of gravitational energy density vanishing in locally inertial frames as per the equivalence principle. The problem is of course that such a pseudo-tensor prescription would fail to be gauge-invariant. One instead works with global quantities that codify the total gravitational energy relative to spatial infinity in asymptotically flat space-times and for which gauge invariance can be imposed using additional constraints.

For stationary, asymptotically flat space-times we can characterize the total gravitational energy by $E = -\frac{1}{8\pi}\int _{S^2_{\infty}} \epsilon_{\mu\nu\alpha\beta}\nabla^{\alpha}\xi^{\beta}$ where $\xi^{\mu}$ is the time-like killing field.

As noted earlier it can be easily shown that for Schwarzschild space-time, $E = M$ where $M$ is the Schwarzschild mass.

 

[tom.stoer]

The discussion regarding gravitational mass M, energy E and the relation E ~ M is far from trivial, and the results are not unambiguously defined for arbitrary spacetimes. Even for stationary and/or asymptotic flat spacetimes like black holes there are several non-trivial problems.

For a comprehensive discussion refer to http://relativity.livingreviews.org/Articles/lrr-2009-4/ , especially chapter 12 - 14.

 

[Naty1]

Quarlep,
If you are still here,the guys have 'gone mathematical' on us!

[Like 'going postal' but for physics peeples, so much more restrained [LOL].]

What you can take away from the earlier posts holds.

The reason you may have thought energy was 'infinite' in a BH is that it appears spacetime curvature [gravity] at the singularity at the 'center' of a BH is 'infinite'. But that's not a good description because the singularity is not well described by any theory we have, not general relativity, not quantum mechanics. So as we get closer and closer to the singularity spacetime curves more and more; we say the curvature 'diverges'...becoming arbitrarily large. That's usually a sign a theory no longer being applicable. This is as we get close to Planck scale.

So as we approach what is believed to be the tinest of scales, the Planck regime, we don't have proper descriptions. Some say space and time and everything else lose their individual meaning as quantum jitters become extreme and all we can so far estimate is a 'quantum foam'...

So the overall energy and gravity of a BH is finite, but the most recent posts are discussing exactly how that should be calculated. People have an analogous problem precisely describing the overall energy in the universe. In curved spacetime, energy, gravity, even time and distance and such become complicated.