Quasilocal conformal Killing horizons: Classical phase space and the first law

TL;DR

This paper develops a framework for describing black hole horizons locally using quasilocal conformal Killing boundaries, constructing the solution space, and establishing a first law analogous to the classical black hole thermodynamics.

Contribution

It introduces a new class of quasilocal horizons with conformal Killing symmetry and derives a corresponding first law within general relativity.

Findings

Constructed a null boundary with conformal Killing vector field.

Identified the solution space admitting such boundaries.

Established a form of the first law for quasilocal horizons.

Abstract

In realistic situations, black hole spacetimes do not admit a global timelike Killing vector field. However, it is possible to describe the horizon in a quasilocal setting by introducing the notion of a quasilocal boundary with certain properties which mimic the properties of a black hole horizon. Isolated horzons and Killing horizons are examples of such kind. In this paper, we construct a boundary of spacetime which is null and admits a conformal Killing vector field. Furthermore we construct the space of solutions (in general theory of relativity) which admits such quasilocal conformal Killing boundaries. We also establish a form of first law for these quasilocal horizons.