Arnowitt-Deser-Misner mass (source code)

= Arnowitt-Deser-Misner mass
{c}
{title2=$M_{\rm ADM}$}

= ADM mass
{c}
{synonym}

For an asymptotically flat stationary solution in its asymptotic rest frame, the <ADM mass> is the gravitational mass measured by the <Arnowitt-Deser-Misner energy>. It is fixed by the asymptotic metric falloff, not by a coordinate parameter's name. If spatial ADM momentum is present, distinguish the asymptotic energy component from the invariant mass obtained from the energy-momentum norm. For a static <Schwarzschild-Tangherlini metric> in $D$ dimensions with $f=1-\mu/r^{D-3}$, the mass is $(D-2)\Omega_{D-2}\mu/(16\pi G_D)$; the dimensional normalization is also reproduced by the <Komar mass normalization in higher dimensions>.