Mechanics of multidimensional isolated horizons

TL;DR

This paper extends the Isolated Horizon framework to arbitrary dimensions, establishing a dimension-independent formulation and deriving the first law of black hole thermodynamics, along with a new energy definition for non-rotating horizons.

Contribution

It provides a dimension-independent formulation of IH mechanics and derives the first law for all dimensions, advancing the understanding of black hole thermodynamics.

Findings

Dimension-independent formulation of IH mechanics

Derivation of the first law of BH thermodynamics in arbitrary dimensions

Proposal of an energy definition for non-rotating horizons

Abstract

Recently a multidimensional generalization of Isolated Horizon framework has been proposed by Lewandowski and Pawlowski (gr-qc/0410146). Therein the geometric description was easily generalized to higher dimensions and the structure of the constraints induced by the Einstein equations was analyzed. In particular, the geometric version of the zeroth law of the black hole thermodynamics was proved. In this work we show how the IH mechanics can be formulated in a dimension--independent fashion and derive the first law of BH thermodynamics for arbitrary dimensional IH. We also propose a definition of energy for non--rotating horizons.