Gravitational radiation from dynamical black holes

TL;DR

This paper introduces an effective energy tensor for gravitational radiation in dynamical black holes, providing a local measure of gravitational energy flux in the strong-field regime.

Contribution

It identifies a new effective energy tensor for gravitational radiation associated with expanding flows of the Hawking mass-energy, applicable near black hole horizons.

Findings

Defines an energy conservation law involving matter and gravitational radiation.

Provides a spin-coefficient formulation for gravitational radiation energy densities.

Establishes a locally unique flow and radiation measure near trapping horizons.

Abstract

An effective energy tensor for gravitational radiation is identified for uniformly expanding flows of the Hawking mass-energy. It appears in an energy conservation law expressing the change in mass due to the energy densities of matter and gravitational radiation, with respect to a Killing-like vector encoding a preferred flow of time outside a black hole. In a spin-coefficient formulation, the components of the effective energy tensor can be understood as the energy densities of ingoing and outgoing, transverse and longitudinal gravitational radiation. By anchoring the flow to the trapping horizon of a black hole in a given sequence of spatial hypersurfaces, there is a locally unique flow and a measure of gravitational radiation in the strong-field regime.