Localisation of Soft Charges, and Thermodynamics of Softly Hairy Black Holes

TL;DR

This paper develops a method to localize large gauge transformation charges within spacetime, leading to new thermodynamic relations for black holes with soft hair, including an intrinsic heat current at the horizon.

Contribution

It introduces a novel approach to localize LGT charges inside spacetime and derives generalized thermodynamic laws for softly hairy black holes.

Findings

Localized LGT charges within spacetime are obtained.

Generalized Smarr formula and first law with angle dependence.

Discovery of an intrinsic heat current at the black hole horizon.

Abstract

Large gauge transformations (LGT) in asymptotically flat space are generated by charges defined at asymptotic infinity. No method for unambiguously localising these charges into the interior of spacetime has previously been established. We determine what this method must be, and use it to find localised expressions for the LGT charges. Applying the same principle to the case of a charged black hole spacetime leads to angle-dependent generalisations of the Smarr formula and the first law of black hole mechanics, both of which have important thermodynamical implications. In particular, the presence of a heat current intrinsic to the event horizon is observed.