11.43 Einstein’s equations
The source of the gravitational field is the energy–momentum tensor Tij. In many astrophysical and most cosmological models, the energy–momentum tensor is assumed to be that of a perfect fluid, which is isotropic in its rest frame, does not conduct heat, and has zero viscosity. For a perfect fluid of pressure p and density ρ with 4-velocity ui (defined by (11.66)), the energy–momentum or stress–energy tensor Tij is
in which gij is the space-time metric.
An important special case is the energy–momentum tensor due to a nonzero value of the energy density of the vacuum. In this case p = –ρ and the energy– ...