Geometry of Generic Isolated Horizons

TL;DR

This paper analyzes the intrinsic geometrical structures of various types of isolated horizons in general relativity, providing tools to extract invariant physical information from numerical simulations of strong gravitational fields.

Contribution

It offers a detailed comparison of horizon geometries and addresses the selection of preferred normals, enhancing the analysis of near horizon physics without relying on previous horizon mechanics results.

Findings

Provides a framework for identifying invariant geometric features of horizons.

Develops tools for extracting physical information from numerical simulations.

Clarifies the role of preferred normals in horizon analysis.

Abstract

Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in detail the issue of singling out the preferred normals to these horizons required in various applications. This work provides powerful tools to extract invariant, physical information from numerical simulations of the near horizon, strong field geometry. While it complements the previous analysis of laws governing the mechanics of weakly isolated horizons, prior knowledge of those results is not assumed.