The energy-momentum tensor

Abstract

Abstract Chapter 12 looks at the three most important energy–momentum tensors in general relativity, namely the energy–momentum tensors for incoherent matter or dust, a perfect fluid, and the electromagnetic field. The treatment is neither exhaustive nor complete, but is sufficient for generating the explicit expressions needed in future chapters. In passing, we look at a tensor formulation of Maxwell’s equations governing the electromagnetic field. It is shown how the electromagnetic energy–momentum tensor can be obtained from a Lagrangian description of the electromagnetic field, which in turn leads to the Einstein–Maxwell equations. This is extended to the case of a general-matter Lagrangian, and various examples are considered. Finally, a physically realistic condition for a matter field called the dominant energy condition is introduced.