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

TL;DR

This work develops a quasi-local, dynamical-horizon framework within full general relativity, deriving local energy and angular-momentum fluxes across dynamical horizons and establishing area, mass, and angular momentum balance laws that generalize Bondi-Sachs-type relations. It defines a generalized angular momentum for cross-sections and shows a corresponding flux balance, and introduces an energy flux decomposition into matter and gravitational parts with a local, non-negative gravitational flux. The authors formulate a physical-process first law for dynamical horizons and identify a canonical Kerr-like mass that reduces to familiar limits (irreducible mass in spherical symmetry and Kerr mass in stationary cases). The results provide practical tools for interpreting and validating numerical simulations of strongly dynamical black holes and extend black hole mechanics to non-stationary spacetimes.

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.