Inner Mechanics of 3d Black Holes

TL;DR

This paper explores the properties of inner horizons in various 3D black holes within higher-derivative gravity theories, confirming the First Law at the inner horizon and analyzing horizon area products in Topologically Massive Gravity.

Contribution

It provides new insights into the inner horizon mechanics of 3D black holes and examines the impact of diffeomorphism anomalies on horizon area relations.

Findings

First Law holds at the inner horizon.

Area product depends on mass in Topologically Massive Gravity.

Diffeomorphism anomaly affects horizon area relations.

Abstract

We investigate properties of the inner horizons of certain black holes in higher-derivative three-dimensional gravity theories. We focus on BTZ and Spacelike Warped Anti-de Sitter black holes, as well as on asymptotically Warped de-Sitter solutions exhibiting both a cosmological and a black hole horizon. We verify that a First Law is satisfied at the Inner horizon, in agreement with the proposal of \cite{Castro:2012av}. We then show that, in Topologically Massive Gravity, the product of the areas of the inner and outer horizons fails to be independent on the mass, and trace this to the diffeomorphism anomaly of the theory.