Observational tests of the black hole area increase law

TL;DR

This paper proposes a method to test the black hole area increase law using gravitational-wave data from black hole mergers, demonstrating its effectiveness with simulated signals and current/future detector sensitivities.

Contribution

It introduces a statistical approach to verify the black hole area theorem with gravitational-wave observations, including a new method to identify the ringdown phase.

Findings

74.6% probability of consistency with current sensitivity

99.9% probability at Advanced LIGO design sensitivity

Method applicable to real gravitational-wave data

Abstract

The black hole area theorem implies that when two black holes merge, the area of the final black hole should be greater than the sum of the areas of the two original black holes. We examine how this prediction can be tested with gravitational-wave observations of binary black holes. By separately fitting the early inspiral and final ringdown stages, we calculate the posterior distributions for the masses and spins of the two initial and the final black holes. This yields posterior distributions for the change in the area and thus a statistical test of the validity of the area increase law. We illustrate this method with a GW150914-like binary black hole waveform calculated using numerical relativity, and detector sensitivities representative of both the first observing run and the design configuration of Advanced LIGO. We obtain a $\sim74.6\%$ probability that the simulated signal is consistent with the area theorem with current sensitivity, improving to $\sim99.9\%$ when Advanced LIGO reaches design sensitivity. An important ingredient in our test is a method of estimating when the post-merger signal is well-fit by a damped sinusoid ringdown waveform.