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

TL;DR

This paper reevaluates the maximum energy emitted as gravitational waves during black hole collisions using black hole thermodynamics, specifically incorporating merging entropy, resulting in a lower upper bound than Hawking's original estimate.

Contribution

It introduces a new approach to estimate gravitational radiation energy bounds by including merging entropy, challenging and refining Hawking's inequality.

Findings

Derived a lower upper bound for gravitational radiation energy.

Showed consistency with numerical simulations of black hole collisions.

Highlighted the importance of merging entropy in black hole thermodynamics.

Abstract

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.