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 Kμ=2ST where the left hand side is the Komar conserved quantity corresponding to the null Killing vector 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.
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