Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions

Understand

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.