# 2 black holes, 2*M -> 1 b.h., 2*M - f*2*M?

• Spinnor
In summary, the conversation discusses the fraction of energy lost as gravitational radiation when two black holes merge. The theoretical upper limit for two identical static black holes is 29% of the initial total mass, but numerical simulations typically show much lower amounts ranging from 0.1% to 14%. For star-sized black holes, the fraction lost is approximately 1/20 of the initial mass. The question of whether this fraction changes with black hole mass is also raised, and a paper discussing gravitational waves from black hole mergers is referenced for further information.
Spinnor
Gold Member
2 black holes, 2*M --> 1 b.h., 2*M - f*2*M?

For equal sized black holes of mass M, what fraction, f, of the energy typically gets lost as gravitational radiation when roughly equal sized black holes merge?

If f were plotted verses mass would the function have a maximum?

Thanks for any help!

For starting point, try page 4 of

http://arxiv.org/abs/0708.4202
Gravitational waves from black-hole mergers
John G. Baker, William D. Boggs, Joan M. Centrella, Bernard J. Kelly, Sean T. McWilliams, James R. van Meter

For two identical static black holes, the rigorous theoretical upper limit is the Hawking bound of (2-√2)m (eg 29% of the initial total mass). Numerical simulations typically show much lower amounts of radiation on the order of 0.1..4% (and up to 14% in the scattering regime).

Last edited:

atyy said:
For starting point, try page 4 of

http://arxiv.org/abs/0708.4202
Gravitational waves from black-hole mergers
John G. Baker, William D. Boggs, Joan M. Centrella, Bernard J. Kelly, Sean T. McWilliams, James R. van Meter

If I follow the paper above, for star sized black holes the fraction lost is about 1/20 the mass of the initial black hole pair. Are there any simple arguments one could give to explain how this fraction changes (or does not change) with black hole mass.

## 1. What are black holes and how do they form?

Black holes are objects in space with such strong gravitational force that even light cannot escape from them. They form when a massive star runs out of fuel and collapses in on itself, creating a singularity with infinite density and a gravitational pull that is strong enough to trap anything that comes too close.

## 2. What happens when two black holes collide?

When two black holes collide, they merge into one larger black hole. This process releases a tremendous amount of energy in the form of gravitational waves, which can be detected by special instruments on Earth.

## 3. How does the mass of a black hole affect its properties?

The mass of a black hole directly affects its size and gravitational pull. The more massive a black hole is, the larger its event horizon (the point of no return for anything that enters) and the stronger its gravitational force. However, all black holes, regardless of mass, have a singularity at their center with infinite density.

## 4. What does "2*M - f*2*M" mean in the context of black holes?

In this context, "2*M" represents the combined mass of two black holes before they merge, and "f*2*M" represents the final mass of the merged black hole. The equation is used to calculate the amount of energy released during a black hole merger.

## 5. Can black holes ever disappear?

According to current theories, black holes do not disappear. They may lose mass through Hawking radiation, but the process is extremely slow and would take a very long time for the black hole to completely evaporate. However, the idea of black hole evaporation is still a topic of ongoing research and debate.

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