Head-on collision and merging entropy of black holes: reconsideration of Hawking's inequality

Understand

We evaluate how much energy can be converted into gravitational radiation in head-on collision of black holes.

• We estimate it by the area theorem of black hole horizon incorporating merging entropy of colliding black holes from a viewpoint of black hole thermodynamics.
• Then we obtain an upper bound of energy ratio of the gravitational radiation which is smaller than the upper bound originally derived by Hawking.
• The fact that this estimation is not inconsistent with the results of both numerical investigations in low- and high-energy head-on collision implies that thermodynamics of coalescing black holes requires the contribution of the merging entropy.