Brown-York quasilocal energy in Lanczos-Lovelock gravity and black hole horizons

TL;DR

This paper extends the Brown-York quasilocal energy concept to Lanczos-Lovelock gravity, verifying an equipartition conjecture for black hole horizons in specific gravity theories and dimensions.

Contribution

It generalizes the Brown-York formalism to all orders in Lanczos-Lovelock gravity and tests the equipartition conjecture across different black hole solutions.

Findings

Equipartition conjecture verified for static charged and axi-symmetric black holes in general relativity.

Generalization of Brown-York energy to all orders in Lanczos-Lovelock theories.

Conjecture holds only for pure Lovelock black holes, not Einstein-Lovelock ones.

Abstract

A standard candidate for quasilocal energy in general relativity is the Brown-York energy, which is essentially a two dimensional surface integral of the extrinsic curvature on the two-boundary of a spacelike hypersurface referenced to flat spacetime. Several years back one of us had conjectured that the black hole horizon is defined by equipartition of gravitational and non-gravitational energy. By employing the above definition of quasilocal Brown-York energy, we have verified the equipartition conjecture for static charged and charged axi-symmetric blck holes in general relativity. We have further generalized the Brown-York formalism to all orders in Lanczos-Lovelock theories of gravity and have verified the conjecture for pure Lovelock charged black hole in all even d=2m+2 dimensions, where m is the degree of Lovelock action. It turns out that the equipartition conjecture works only for pure Lovelock, and not for Einstein-Lovelock, black holes.