Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions

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 $K_{χ^μ}=2ST$ where the left hand side is the Komar conserved quantity corresponding to the null Killing vector $χ^μ$ 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.

v3, minor changes over v2, LaTex, 16 pages, no figures, to appear in Phys. Rev. D