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Stress-Energy Tensor

The stress-energy tensor

T_{ u ho au u}

represents the density and flux of energy and momentum in spacetime, dictating the gravitational field.

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The statement of the theorem

The stress-energy tensor

T_{\mu\nu}

is a rank-2 symmetric tensor defined by the variation of the Lagrangian density

\mathcal{L}

with respect to the metric

g_{\mu\nu}

, representing the density and flux of energy and momentum:\n

T_{\mu\nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}}{\delta g^{\mu\nu}}

\nIt satisfies the conservation law:\nabla^{\mu} T_{\mu\nu} = 0$.