In the case when the

energy-momentum tensor is present (supposing however that it describes the influence of matter weak enough in order to keep the basic solution unchanged), one must use the full Einstein's tensor on the right-hand side.

Its 4-curvature is determined from the various contributions to its total

energy-momentum tensor density, namely in the form of matter energy density, radiation pressure and cosmological constant.

mu]v] is the

energy-momentum tensor of matter, c is the light speed in free space, and G is the gravitational constant.

In general relativity the matter content of the spacetime is described by the

energy-momentum tensor T which is to be determined from the physical considerations dealing with the distribution of matter and energy.

Ueno begins by describing Riemann spaces and stable curves, including compact Riemann surfaces and pointed curves, then moves to affine Lie algebras and integrable highest weight representations, with an explanation of the

energy-momentum tensor, Uechi then moves to conformal blocks and correlation functions, the sheaf of conformal blocks associated with a family of pointed Reimann surfaces with coordinates, the sheaf's support of projectively flat connections, one of the most important facts of conformal field theory.

We write the conservation law for the Einstein tensor density derived from the Bianchi identities, which cannot apply to the

energy-momentum tensor density as a source;

The

energy-momentum tensor of the electromagnetic field at macroscopic scales [section]4.

Using this notation and taking into account that in the surrounding spacetime of the material particle there is an electric current j, as given by equation (242), the

energy-momentum tensor [19-21] of the electromagnetic field is given by the tensor

This, of course, is part of the the emergence of a purely geometric

energy-momentum tensor as well.

alpha][beta]] is the

energy-momentum tensor, and [alpha], [beta] = 0, 1, 2, 3 are the space-time indices.

Thus, the

energy-momentum tensor of the system will thus be chosen to be

Montesinos and Flores [9] deduce the electromagnetic

energy-momentum tensor via Noether's theorem [10].