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When a body falls into a black hole, the black hole's mass increases. Does this mass increase depend only on the rest mass of the infalling object, or is it affected by the velocity of the infalling mass. Of course, if it is velocity dependent, then does it depend on the relative velocity between the black hole and the infaller or the velocity between the infalling mass and an external observer. If the second situation is the case, is the mass of a black hole dependent on an external frame's velocity relative to everything that has ever fallen into it (seems highly unlikely)? If it is not velocity dependant, then what happens to the excess kinetic energy (measured say, in an accelerated frame of reference at a constant distance from the black hole)?

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It is basically the same as two ordinary objects colliding and sticking together. The combined object's rest mass is the sum of the total energy of the original objects in the center-of-mass frame, which is their rest mass/energy plus their kinetic energy in that frame. Some of that would be carried away as gravitational radiation, but typically only a small amount, I think.

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