Isolated and dynamical horizons from a common perspective

TL;DR

This paper develops a unified framework for the constraint equations on three-dimensional hypersurfaces, applicable to both isolated and dynamical horizons, enabling the extraction of physical quantities regardless of horizon type.

Contribution

It introduces a common perspective and equations for analyzing isolated and dynamical horizons, including perturbations and exact solutions.

Findings

Derived equations for horizons of arbitrary signature

Framework for extracting physical quantities from horizons

Presented a family of axially-symmetric solutions

Abstract

A framework is developed in which one can write down the constraint equations on a three--dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract physicaly relevant quantities describing the horizon irrespective to whether it is isolated (null) or dynamical at a given instant of time. Furthermore, small perturbation of isolated horizons are considered, and finally a family of axially--symmetric exact solution of the constraint equations on a dynamical horizon is presented.