Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions

TL;DR

This paper derives a new identity relating Komar conserved quantities to black hole entropy and temperature in arbitrary dimensions, and establishes a generalized Smarr formula connecting black hole parameters with thermodynamic properties.

Contribution

It introduces a novel identity for Komar quantities at the horizon and derives a generalized Smarr formula for higher-dimensional charged rotating black holes.

Findings

New identity: $K_{\chi^{\mu}}=2ST$ at the horizon

Generalized Smarr formula for $M, J, Q$ in arbitrary dimensions

Validation of the formula through algebraic methods

Abstract

We calculate the effective Komar conserved quantities for the $N+1$ dimensional charged Myers-Perry spacetime. At the event horizon we derive a new identity $K_{\chi^{\mu}}=2ST$ where the left hand side is the Komar conserved quantity corresponding to the null Killing vector $\chi^{\mu}$ while in the right hand side $S,~T$ are the black hole entropy and Hawking temperature. From this identity we also derive the generalized Smarr formula connecting the macroscopic parameters $M,~J,~Q$ of the black hole with its surface gravity and horizon area. The consistency of this new formula is established by an independent algebraic approach.