= Komar mass normalization in higher dimensions
{c}
{title2=$M=-\frac{D-2}{16\pi G_D(D-3)}\int\nabla^ak^b\,d\Sigma_{ab}$}
For future static-slice normal $u$ and outward radial normal $n$, take $d\Sigma_{ab}=(n_au_b-n_bu_a)dA$, with both antisymmetric components summed. For the <Schwarzschild-Tangherlini metric> the flux is $-\Omega_{D-2}r^{D-2}f'=-(D-3)\Omega_{D-2}\mu$. 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.
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