Isolated Horizons: Hamiltonian Evolution and the First Law

TL;DR

This paper extends the isolated horizons framework to include distorted and rotating horizons, develops a new Hamiltonian analysis, and shows the first law as a condition for consistent evolution, leading to new insights for static black holes.

Contribution

It significantly extends the isolated horizons framework by incorporating rotation and distortion, and establishes the first law as a key condition for Hamiltonian evolution.

Findings

First law arises as a necessary and sufficient condition for Hamiltonian evolution.

New predictions for static black holes based on the consistency condition.

Framework now includes non-rotating, rotating, and distorted horizons.

Abstract

A framework was recently introduced to generalize black hole mechanics by replacing stationary event horizons with isolated horizons. That framework is significantly extended. The extension is non-trivial in that not only do the boundary conditions now allow the horizon to be distorted and rotating, but also the subsequent analysis is based on several new ingredients. Specifically, although the overall strategy is closely related to that in the previous work, the dynamical variables, the action principle and the Hamiltonian framework are all quite different. More importantly, in the non-rotating case, the first law is shown to arise as a necessary and sufficient condition for the existence of a consistent Hamiltonian evolution. Somewhat surprisingly, this consistency condition in turn leads to new predictions even for static black holes. To complement the previous work, the entire discussion is presented in terms of tetrads and associated (real) Lorentz connections.