Gravitational Calorimetry

TL;DR

This paper extends the quasilocal thermodynamic formulation to a broad class of gravity theories with matter fields, enabling analysis of diverse black hole spacetimes including non-asymptotically flat and rotating solutions.

Contribution

It generalizes Brown and York's thermodynamic approach to include dilaton and gauge fields, applicable to various theories and complex black hole configurations.

Findings

Thermodynamic variables computed for multiple black hole solutions.

Formalism handles non-asymptotically flat and rotating black holes.

Inclusion of dilaton, electric, and magnetic charges in thermodynamic analysis.

Abstract

I generalize the quasilocal formulation of thermodynamics of Brown and York to include dilaton theories of gravity as well as Abelian and Yang-Mills gauge matter fields with possible dilaton couplings. The resulting formulation is applicable to a large class of theories including two-dimensional toy models and the low energy limit of string theory as well as to many types of matter such as massless scalar fields, electromagnetism, Yang-Mills fields, and matter induced cosmological constants. I use this formalism to evaluate the thermodynamic variables for several black hole spacetimes. I find that the formulation can handle black hole spacetimes that are not asymptotically flat as well as rotating black hole spacetimes, and black hole spacetimes possessing a dilaton field, an electric charge, and a magnetic charge.