Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations

TL;DR

This paper develops a unified geometric framework for analyzing isolated and dynamical trapping horizons, deriving flux laws and characterizing slowly evolving horizons with a dynamical first law similar to the Hawking-Hartle formula.

Contribution

It introduces a common framework for the geometry and dynamics of trapping horizons, unifies existing results, and derives new insights into slowly evolving horizons and their flux laws.

Findings

Characterization of slowly evolving horizons

Derivation of a dynamical first law for these horizons

Unification of known results on trapping horizons

Abstract

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the "almost-isolated" trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.