Komar mass normalization in higher dimensions ($M=-\frac{D-2}{16\pi G_D(D-3)}\int {\nabla }^a{k}^{b}d{\Sigma }_{ab}$)

For future static-slice normal $u$ and outward radial normal $n$, take $d{\Sigma }_{ab}=(n_a{u}_b-n_b{u}_a)dA$, with both antisymmetric components summed. For the Schwarzschild-Tangherlini metric the flux is $-{\Omega }_{D-2}{r}^{D-2}{f}^{\prime }=-(D-3){\Omega }_{D-2}\mu$. The displayed dimension-dependent coefficient then reproduces the ADM mass. Reversing orientation reverses the flux; including a factor of one-half in the binormal convention also changes its numerical value. A four-dimensional normalization cannot be carried unchanged into other dimensions.