Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws

TL;DR

This paper develops local flux formulas for energy and angular momentum across dynamical horizons in full general relativity, generalizing classical black hole laws and relating horizon area changes to gravitational wave fluxes.

Contribution

It introduces new flux expressions for dynamical horizons in non-linear general relativity, extending classical laws of black hole mechanics.

Findings

Fluxes of energy and angular momentum are positive and local.

Horizon area change is directly related to fluxes of gravitational waves.

Balance laws analogous to Bondi and Sachs are derived for dynamical horizons.

Abstract

Dynamical horizons are considered in full, non-linear general relativity. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local, the energy flux is positive and change in the horizon area is related to these fluxes. The flux formulae also give rise to balance laws analogous to the ones obtained by Bondi and Sachs at null infinity and provide generalizations of the first and second laws of black hole mechanics.