Geometry of Non-expanding Horizons and Their Neighborhoods

TL;DR

This paper develops a geometric framework for non-expanding horizons, constructing special frames and coordinates that reveal invariants, degrees of freedom, and conditions for symmetries, advancing understanding of horizon geometry.

Contribution

It introduces a new geometric construction of frames and coordinates on non-expanding horizons, identifying invariants and symmetry conditions.

Findings

Constructed distinguished frames and coordinates on horizons.

Identified free degrees of freedom and invariants.

Derived existence conditions for Killing vectors.

Abstract

This is a contribution to MG9 session BHT4. Certain geometrically distinguished frame on a non-expanding horizon and in its space-time neighborhood, as well as the Bondi-like coordinates are constructed. The construction provides free degrees of freedom, invariants, and the existence conditions for a Killing vector field. The reported results come from the joint works with Ashtekar and Beetle.