General Relativity: An Introduction for Physicists · Problem 8.1

The gravitational field equations — Hobson, Efstathiou & Lasenby

Physics · energy-momentum-tensor-perfect-fluid

Problem

Show that the components of the energy–momentum tensor of a perfect fluid in its instantaneous rest frame can be written as in (8.3):

T^{\mu\nu} = (\rho + p/c^2)u^\mu u^\nu - p\eta^{\mu\nu}.

Can the components be written in any other covariant form?