B Black Hole Energy Conversion - How Does It Work?

[Peter Cole]

TL;DR Summary

How does a black hole convert mass into energy?

If you search on-line for "efficiency of a black hole" you will get several discussions suggesting that the efficiencies of converting mass to energy are from 6% for non-rotating black holes to 42% for the fastest rotating black holes. I would like to know exactly how black holes convert some of their mass into energy. I would think that most of the energy conversion/loss is done within a black hole's accretion disk. I'm sure there is also some energy loss when jets are created but because their creation is not well understood I would be more interested in the energy conversion/loss done in accretion disks.

 

[Ibix]

It's hard to guess what you want to talk about from "there are some articles" and a vague paraphrase. Please provide links to what you want to discuss.

 

[Dale]

Summary:: How does a black hole convert mass into energy?

If you search on-line for "efficiency of a black hole" you will get several discussions suggesting that the efficiencies of converting mass to energy are from 6% for non-rotating black holes to 42% for the fastest rotating black holes

I agree with @Ibix about needing the references. Especially the one claiming 6% and the one claiming 42%.

 

[Peter Cole]

I did not expect that the values of 6% and 42% would prevent the answering of my question. I thought I was being careful saying "several discussions suggesting" concerning the figures meaning that I neither confirmed nor denied they were true or false. However since you asked me to provide where I found the figures I will try to do so. My search engine is DuckDuckGo and using "efficiency of a black hole" on that search engine I was able to find the following that mentions both figures:

http://large.stanford.edu/courses/2016/ph240/morningstar2/

I have no idea what "vague paraphrase" means so will not be able to respond to that comment by Ibix.

Hopefully this will allow the answering of my question which was "How does a black hole convert mass into energy?".

 

[PeterDonis]

I thought I was being careful saying "several discussions suggesting" concerning the figures meaning that I neither confirmed nor denied they were true or false.

It's not a matter of whether they are true or false. It's a matter of you having read whatever references you have read but not us. We need to read the same references you are reading in order to be able to give you any useful feedback about what they say. Just saying the phrase "black hole converts mass to energy" does not give us enough information to make any useful response.

I have no idea what "vague paraphrase" means

It means that, instead of giving us the actual references you read so we can read them for ourselves, you tried to describe what they were saying in your own words. It is much better to just give us the references.

 

[Ibix]

I thought I was being careful saying "several discussions suggesting" concerning the figures meaning that I neither confirmed nor denied they were true or false.

The point of a reference is that we are all working from the same source. We can criticize the source, or understand what limits or assumptions there are in it. We can't do that from a summary in a forum post (unless it's one of the evergreen topics we have here).

How does a black hole convert mass into energy?

It doesn't, really. Frictional processes (that is, random collisions between molecules) in the accretion disc cause the orbiting gas to slow down, emitting radiation which could (in principle) be captured and used. The article simply says that the energy available to be released this way is the gravitational potential energy difference between infinity and the innermost stable orbital radius (arguing that inside that radius the matter more or less drops straight into the hole without time to radiate). Different types of black holes have different innermost stable orbits, so different amounts of energy could be released this way.

Note that the particular reference you provide appears to be a piece of coursework. It hasn't been peer reviewed and doesn't have a mark attached. It seems reasonable at first glance, but I wouldn't have high confidence in it without a lot more thought than I've given this.

 

[PeterDonis]

I would like to know exactly how black holes convert some of their mass into energy.

The article you gave a link to in post #4 gives the following paper by Martin Rees as a reference for the 6% and 42% figures:

https://www.annualreviews.org/doi/abs/10.1146/annurev.aa.22.090184.002351

As the article says, and as the paper discusses in more detail, for a non-rotating hole, the 6% figure comes from gravitational binding energy, considered as a fraction of rest mass: basically, we imagine an idealized process where an object with some rest mass $m$ goes from rest at infinity into a circular orbit about the black hole at some radius $r$. This process requires extracting energy from the object, and if we pick the radius of the circular orbit appropriately, we can maximize the amount of energy that can be extracted. That amount is 6% of the object's rest mass, corresponding to a radius of 3 times the Schwarzschild radius of the hole. (Once the object is in that circular orbit, in the idealized process, no further energy can be extracted from it; it will just stay in that orbit until some small perturbation kicks it towards the hole and it falls in, but that process yields no energy.)

The 42% figure for a rotating hole comes from applying a similar argument but using parameters for Kerr spacetime instead of Schwarzschild spacetime, in the limit where the hole is rotating at the maximum angular velocity it can rotate and still have an event horizon. The closest stable circular orbit approaches the horizon radius in this limit, which is why the percentage is significantly larger than for the Schwarzschild case.

(Note, btw, that Rees' notation might be somewhat confusing. He uses the notation $r_g$ to refer to the quantity $GM / c^2$, the black hole's mass converted to a length. It is more typical to see a notation like $r_g$ or $r_s$ used to refer to the Schwarzschild radius of the hole, which is $2 GM / c^2$, i.e., twice as large as Rees's $r_g$. In the above I have phrased things in terms of the Schwarzschild radius.)

 

[Dale]

I did not expect that the values of 6% and 42% would prevent the answering of my question.

It is not the values, it is the context. You are asking how something fairly generic happens and the reference with the 6% might be discussing a very different specific mechanism than the 42% reference. Without the actual references we are just guessing which of all possible mechanisms is being described.

In any case asking for and providing references is just part of the culture of this forum. It is not a negative reflection on you or your question.

I was able to find the following that mentions both figures:

http://large.stanford.edu/courses/2016/ph240/morningstar2/

I looked in there and followed up with the paper that it referenced which is: https://www.annualreviews.org/doi/pdf/10.1146/annurev.aa.22.090184.002351

Summary:: How does a black hole convert mass into energy?

I would like to know exactly how black holes convert some of their mass into energy.

So those two figures are nothing particularly exotic. It is just lowering the potential energy of the infalling matter and radiating out the energy, typically as thermal radiation.

Basically, as a dust cloud collapses the individual particles start out cold and in elliptical orbits. Then they fall inward converting PE to KE. While they are low they are traveling very fast and collisions are likely. In those collisions they lose KE and gain thermal energy. As they slow they enter a circular orbit and collisions are reduced. So overall they have converted gravitational PE to thermal energy which can radiate away.

The 6% figure is for a non rotating black hole. The 42% figure is the maximum for co-rotating material falling towards a black hole that is spinning at the fastest possible rate. Nothing exotic is happening with the material, just the orbits are exotic due to relativistic effects like frame dragging.

Edit: I see @PeterDonis followed the trail to the same reference.

 

[hmmm27]

So, how does evaporation fit in ?

 

[Dale]

So, how does evaporation fit in ?

It doesn't factor into this mechanism at all. That is partly why I wanted a reference. Hawking evaporation was the first thing that came to my mind also.