Charges in General Relativity and Black Hole Thermodynamics

TL;DR

This paper develops a covariant phase space formalism in General Relativity that accounts for boundary fluctuations, revealing how charges relate to background independence and extending black hole thermodynamics laws without traditional assumptions.

Contribution

It introduces a new covariant phase space approach allowing boundary fluctuations, providing a generalized derivation of black hole thermodynamics laws.

Findings

Charges are linked to integration constants breaking background independence.

Generalized first law of black hole thermodynamics without bifurcation surface assumptions.

First principles derivation of the Smarr relation within the new framework.

Abstract

We shed a new light on the longstanding problem of covariant charges in diffeomorphism invariant theories like General Relativity (GR) by noting the other important feature of the theory, the background independence. To this end, we develop covariant phase space formalism in which we allow for the boundaries of spacetime to have arbitrary fluctuations. Within this formalism we show non-covariance of charges appear in inevitable integration constants which also break background independence in the expression of charges. We then apply the same formalism to black hole thermodynamics. We generalize the seminal Iyer-Wald derivation the first law of bl1ack hole thermodynamics by relaxing the need for the assumptions at a bifurcation surface and asymptotic infinity, as well as addressing questions regarding the integrability of charges. We also present a first principles derivation of the Smarr relation within our framework.