Generalized Smarr formula as a local identity for arbitrary dimensional black holes

TL;DR

This paper introduces a local identity at the event horizon of black holes in arbitrary dimensions, derived from Killing symmetries and Komar charges, which generalizes the Smarr formula in a purely local manner.

Contribution

It presents a new local identity at black hole horizons that generalizes the Smarr formula for arbitrary dimensional charged, rotating black holes, linking it to emergent gravity.

Findings

Derivation of a local horizon identity in Einstein-Maxwell gravity.

The local identity reproduces the generalized Smarr formula.

Potential connections to emergent gravity theories.

Abstract

We discuss a method based on Killing symmetries and Komar conserved charges to generalize Smarr mass formula for arbitrary dimensional charged, rotating spacetime. We derive a local identity defined at the event horizon of the rotating black hole in Einstein-Maxwell gravity which reproduces the generalized Smarr formula as a by-product. The advantages of this new identity are the following: (i) unlike Smarr formula, which is non-local, this identity is purely local and hence a switchover between horizon and infinity is unnecessary and (ii) the new identity could be mapped with the recent investigations on emergent gravity.