General Relativity: An Introduction for Physicists · Problem 17.17

Linearised general relativity — Hobson, Efstathiou & Lasenby

Physics · stationary-source-momentum-integral-identity

Problem

For a stationary source, show that

\partial_0 T^{0i} = 0

. Hence show that

\int_V (T^{0i}y^j + T^{0j}y^i)\, d^3\vec{y} = 0,

where the spatial volume

V

encloses the source.