Quasilocal Corrections to Bondi's Mass-Loss Formula and Dynamical Horizons

TL;DR

This paper introduces quasilocal corrections to Bondi's mass-loss formula using a null geometric approach, revealing new insights into energy transfer at dynamical horizons in non-stationary spacetimes.

Contribution

It derives an integral law for mass and energy change at dynamical horizons, showing quasilocal corrections to Bondi's formula and clarifying energy transfer mechanisms.

Findings

Energy transfer rate vanishes at equilibrium horizons.

New quasilocal correction terms to Bondi mass-loss formula.

Simplified integral expressions for Generalized Vaidya spacetimes.

Abstract

In this work, a null geometric approach to the Brown-York quasilocal formalism is used to derive an integral law that describes the rate of change of mass and/or radiative energy escaping through a dynamical horizon of a non-stationary spacetime. The result thus obtained shows - in accordance with previous results from the theory of dynamical horizons of Ashtekar et al. - that the rate at which energy is transferred from the bulk to the boundary of spacetime through the dynamical horizon becomes zero at equilibrium, where said horizon becomes non-expanding and null. Moreover, it reveals previously unrecognized quasilocal corrections to the Bondi mass-loss formula arising from the combined variation of bulk and boundary components of the Brown-York Hamiltonian, given in terms of a bulk-to-boundary inflow term akin to an expression derived in an earlier paper by the author [#huber2022remark]. For clarity, this is discussed with reference to the Generalized Vaidya family of spacetimes, for which derived integral expressions take a particularly simple form.