Horizon Mechanics and Asymptotic Symmetries with a Immirzi-like Parameter in 2+1 Dimensions

TL;DR

This paper explores how an Immirzi-like parameter modifies black hole mechanics and asymptotic symmetries in 2+1 dimensional gravity, providing new insights into horizon properties and covariant phase space analysis.

Contribution

It introduces a generalized 2+1 gravity theory with an Immirzi-like parameter and derives modified black hole laws and asymptotic symmetries within a covariant framework.

Findings

Modified laws of black hole mechanics due to the Immirzi-like parameter

Natural definitions of horizon mass and angular momentum

Analysis of asymptotic symmetries in covariant phase space

Abstract

Starting with a generalized theory of 2+1 gravity containing an Immirzi like parameter, we derive the modified laws of black hole mechanics using the formalism of weak isolated horizons. Definitions of horizon mass and angular momentum emerge naturally in this framework. We further go on to analyze the asymptotic symmetries, as first discussed by Brown and Henneaux, and analyze their implications in a completely covariant phase space framework.