Calculating M from Charge & Angular Momentum in Black Hole

In summary, the parameters of a general black hole, including mass, charge, and angular momentum, all contribute to the overall mass. If a massless charge is added to a Schwarzschild black hole, the mass will increase due to the compression of like-signed charges. Similarly, angular momentum also contributes to the mass, as objects with angular momentum in the same direction are partially repelled by the rotating black hole. The work required to bring the charge up to the event horizon is equal to the mass gain. However, for naked black holes, the concept of mass from these sources breaks down. There is also an equation for finding the irreducible mass, and when the black hole is extremal, the quantities for mass, angular momentum,
  • #1
michael879
698
7
Ok so this has always confused me and I still can't seem to find an answer anywhere! A general black hole has parameters M, Q, and J which are given the meaning of mass, charge, and angular momentum. My question is what what is the contribution to M by Q and J?? Presumably if you start with a Schwarzschild black hole and drop "massless" charge (not possible in reality but electrons at rest come pretty close) into it, it will not only gain charge but M will be increased due to the compression of like-signed charges. The situation is similar for angular momentum where a rotating black hole partially repels objects with angular momentum in the same direction. The extra energy required to get the object into the black hole should add to M.

So how much of M is due to charge and angular momentum, and how would you go about calculating it? Naively I would guess that the mass gain is equal to the work required to bring the charge up to the event horizon (since no energy can escape whatever happens within the horizon can't increase the mass).
 
Physics news on Phys.org
  • #3
Thanks, that's an interesting way to look at it. I'm a little curious why the entire concept would break down for naked black holes though. As far as I know GR allows for the existence of naked black holes. However if you look at the fraction of mass from the 3 "sources" as a black hole becomes extremal and then naked, you see some strange behavior.. An extremal black hole has 1/2 of its mass from charge/angular momentum and 1/2 from the "static" term. However once you lose the event horizon the entire equation breaks down and Q and J no longer appear to contribute to the mass at all!
 
  • #4
WannabeNewton has probably already answered the question but another source for finding the irreducible mass (Mir) is here-

http://www.ece.uic.edu/~tsarkar/Goodies/Black Hole.pdf page 12 eq. 10

and when the black hole is extremal (i.e. M2=a2+Q2), quantities for M, J and Q still hold (where J=aM)
 
  • #5


Thank you for your question. The contribution of charge and angular momentum to the mass of a black hole is a complex and ongoing topic of research in the field of black hole physics. The concept of black hole mass itself is somewhat ambiguous, as the mass we observe is actually the gravitational mass, which is related to the total energy of the black hole, including its mass, charge, and angular momentum.

In general, the contribution of charge and angular momentum to the mass of a black hole can be calculated using the Kerr-Newman metric, which describes a rotating and charged black hole. This metric takes into account the effects of both charge and angular momentum on the spacetime around the black hole. However, this calculation is not straightforward and requires advanced mathematical techniques.

Additionally, it is important to note that the contribution of charge and angular momentum to the mass of a black hole is not a simple additive process. As you mentioned, the addition of charge or angular momentum to a black hole can also affect its mass due to the compression of like-signed charges or the repulsion of objects with angular momentum in the same direction. This means that the relationship between mass, charge, and angular momentum in a black hole is highly non-linear and cannot be easily quantified.

In summary, while we have theoretical models and calculations that can give us an idea of the contribution of charge and angular momentum to the mass of a black hole, it is a complex and ongoing area of research that requires further study and development.
 

1. How is charge and angular momentum related to the mass of a black hole?

The mass of a black hole can be calculated using the formula M = (Q^2 + J^2) / 2, where Q is the charge and J is the angular momentum of the black hole.

2. Can the charge and angular momentum of a black hole be measured?

Yes, the charge and angular momentum of a black hole can be measured indirectly through their effects on the surrounding matter and light. Scientists use various techniques, such as analyzing the motion of nearby objects, to estimate these values.

3. How do scientists determine the charge and angular momentum of a black hole?

One method is to study the behavior of particles near the event horizon of a black hole. The charge and angular momentum of a black hole can also be estimated by observing the shape and size of the black hole's accretion disk.

4. Is there a limit to the amount of charge and angular momentum a black hole can have?

Yes, according to the Kerr-Newman metric, there is a limit to the amount of charge and angular momentum a black hole can have. This limit is known as the extremal limit and any black hole with a charge or angular momentum beyond this limit is considered to be a naked singularity.

5. Can the mass of a black hole change over time?

Yes, the mass of a black hole can change over time as it absorbs matter and energy from its surroundings. This process, known as accretion, can cause the black hole to grow in mass and alter its charge and angular momentum as well.

Similar threads

  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
3
Views
977
  • Special and General Relativity
Replies
11
Views
639
  • Special and General Relativity
2
Replies
62
Views
3K
  • Special and General Relativity
Replies
1
Views
871
  • Special and General Relativity
Replies
5
Views
488
  • Special and General Relativity
Replies
3
Views
770
  • Special and General Relativity
Replies
4
Views
788
  • Special and General Relativity
Replies
4
Views
907
  • Special and General Relativity
Replies
18
Views
1K
Back
Top