Killing symmetries and Smarr formula for black holes in arbitrary dimensions

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.