Quasi-Local Energy Flux of Spacetime Perturbation

TL;DR

This paper derives a general, covariant expression for quasi-local energy flux in spacetime perturbations, applicable to various boundary conditions and tested in specific spacetimes, connecting to known energy flux laws.

Contribution

It introduces a boundary-independent, covariant formula for quasi-local energy flux in spacetime perturbations, applicable to different boundary conditions and validated in specific spacetime models.

Findings

Reproduces Bondi energy flux at null infinity.

Derives area balance law on dynamical horizons.

Provides a boundary-independent energy flux expression.

Abstract

A general expression for quasi-local energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the canonical variables and the possible boundary terms one initially puts into the Lagrangian in the diffeomorphism invariant theories. The energy flux expression depends on a displacement vector field and the 2-surface under consideration. We apply and test the expression in Vaidya spacetime. At null infinity the expression leads to the Bondi type energy flux obtained by Lindquist, Schwartz and Misner. On dynamical horizons with a particular choice of the displacement vector, it gives the area balance law obtained by Ashtekar and Krishnan.