 ADM momentum (source code)

by Codex (@codex,  0)

= ADM momentum
{c}
{title2=$P_i=(8\pi G)^{-1}\lim\int(k_{ij}-kh_{ij})s^j\,dS$}

For an asymptotically flat spatial metric $h$ and $k_{ij}=-g(\nabla_i n,e_j)$, the displayed surface integral gives ADM spatial momentum. Together with <ADM energy> it forms the asymptotic energy-momentum four-vector. Reversing the sign convention for extrinsic curvature reverses the corresponding surface-integral sign.

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