Mathematics of General Relativity - The Energy-momentum Tensor

The Energy-momentum Tensor

The sources of any gravitational field (matter and energy) are represented in relativity by a type (0, 2) symmetric tensor called the energy-momentum tensor. It is closely related to the Ricci tensor. Being a second rank tensor in four dimensions, the energy-momentum tensor may be viewed as a 4 by 4 matrix. The various admissible matrix types, called Jordan forms cannot all occur, as the energy conditions that the energy-momentum tensor is forced to satisfy rule out certain forms.