Distorted black holes: nonextensivity in the gravitational wave emission

TL;DR

This paper models the interaction of gravitational waves with black holes using Einstein's equations, revealing how black holes absorb mass and establishing a nonextensive relation for the absorbed mass based on initial wave parameters.

Contribution

It introduces a novel nonextensive relation for black hole mass absorption during gravitational wave interactions, using the characteristic formulation of Einstein's equations.

Findings

Black holes form apparent horizons after sufficient mass accretion.

The final black hole mass can be quantified from initial gravitational wave data.

A nonextensive relation describes the absorbed mass as a function of initial parameters.

Abstract

We investigate the interaction between a non-rotating black hole and incoming gravitational waves using the characteristic formulation of the Einstein field equations, framed as a Bondi problem. By adopting retarded time as the null coordinate and recognizing that the final state is invariably a black hole, we show that an apparent horizon forms once sufficient mass accretes onto the black hole. We derive the evolution of the Bondi mass and compute its final value, enabling us to quantify the fraction of the incident mass absorbed by the black hole. Additionally, we establish a nonextensive relation for the absorbed mass as a function of initial parameters, such as the amplitude of the gravitational wave data.