Mass correction and gravitational energy radiation in black hole perturbation theory

TL;DR

This paper demonstrates that in second order black hole perturbation theory, the difference between ADM mass and final black hole mass equals the total gravitational radiation energy, confirming the theory's consistency.

Contribution

It establishes a link between mass difference and gravitational radiation energy in second order perturbation theory, serving as a consistency check.

Findings

Mass difference equals gravitational radiation energy to lowest order

Validates the consistency of second order black hole perturbation theory

Uses Landau and Lifschitz pseudotensor method for energy calculation

Abstract

Using second order black hole perturbation theory, we show that the difference between the ADM mass and the final black hole mass, computed to the lowest significant order, is equal, to the same order, to the total gravitational radiation energy, obtained applying the Landau and Lifschitz (pseudotensor) equation to the first order perturbation. This result may be considered as a consistency check for the theory.