Kerr-Newman Black Hole Thermodynamical State Space: Blockwise Coordinates

TL;DR

This paper develops a simplified coordinate system for analyzing the thermodynamical state space of Kerr-Newman black holes, revealing symmetries and limiting cases that connect to simpler black hole models.

Contribution

It introduces a blockwise coordinate system that simplifies the Kerr-Newman thermodynamical metric and extends known symmetries from simpler black holes to the general case.

Findings

Identifies a coordinate system that simplifies the Kerr-Newman thermodynamical metric.

Shows the survival of a conformal Killing vector in the generalized case.

Connects the Kerr-Newman case to limiting cases of Reissner-Nordstrom and Kerr black holes.

Abstract

A coordinate system that blockwise-simplifies the Kerr-Newman black hole's thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner-Nordstrom and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr-Newman case's 3 by 3 thermodynamical state space metric.