Quasi-local rotating black holes in higher dimension: geometry

TL;DR

This paper generalizes the theory of non-expanding and isolated horizons to higher-dimensional spacetimes, providing a local geometric description and deriving thermodynamic laws for such black holes.

Contribution

It extends the definitions and properties of horizons from 4D to higher dimensions, including a local geometric framework and thermodynamic laws.

Findings

Generalized Raychaudhuri equation for higher dimensions

Derived the Zeroth Law of black hole thermodynamics in higher dimensions

Provided a local geometric description of higher-dimensional horizons

Abstract

With a help of a generalized Raychaudhuri equation non-expanding null surfaces are studied in arbitrarily dimensional case. The definition and basic properties of non-expanding and isolated horizons known in the literature in the 4 and 3 dimensional cases are generalized. A local description of horizon's geometry is provided. The Zeroth Law of black hole thermodynamics is derived. The constraints have a similar structure to that of the 4 dimensional spacetime case. The geometry of a vacuum isolated horizon is determined by the induced metric and the rotation 1-form potential, local generalizations of the area and the angular momentum typically used in the stationary black hole solutions case.