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

Understand

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.