Constraining black hole horizon effects by LIGO-Virgo detections of inspiralling binary black holes

Abstract

General relativity predicts mass and spin growth of an inspiralling black hole due to an energy-momentum flux flowing through the black-hole horizon. The leading-order terms of this horizon flux introduce 2.5 and 3.5 post-Newtonian corrections to inspiral motions of binary black holes. The corrections may be measurable by gravitational waves detectors. Since the proper improvements to general relativity is still a mystery, it is possible that the true modified gravity theory introduces negligible direct corrections to the geodesics of test masses, while near horizon corrections are observable. We introduce a parameterization to describe arbitrary mass and spin growth of inspiralling black holes. Comparing signals of gravitational waves and a waveform model with parameterized horizon flux corrections, deviations from general relativity can be constrained. We simulate a set of gravitational waves signals following an astrophysical distribution with horizon flux modifications. Then, we perform a Bayesian analysis to obtain the expected constraints from the simulated response of the Advanced LIGO-Virgo detector network to the simulated signals. We show that the constraint can be improved by stacking multiple detections. The constraints of modified horizon flux can be used to test a specific class of modified gravity theories which predict dominant corrections near black-hole horizons over other types of corrections to general relativity. To support Hawking's area theorem at 90\% confidence level, over 10000 LIGO-Virgo detections are required. Within the lifetime of LIGO and Einstein Telescope, a future ground-based gravitational wave detector, near horizon corrections of modified gravity theories are potentially detectable if one of the modified gravity theory is true and the theory predicts a strong correction.