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Conservation of Energy-Momentum

The divergence of the stress-energy tensor is zero, reflecting the conservation of energy and momentum within the framework of General Relativity.
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The statement of the theorem

Let TμνT_{\mu\nu} be the stress-energy tensor describing the distribution of energy and momentum. The conservation of energy and momentum in curved spacetime is expressed by the vanishing of the covariant divergence of TμνT_{\mu\nu}:\n\n∇μTμν=0\nabla_{\mu} T^{\mu\nu} = 0 \n\nWhere ∇μ\nabla_{\mu} is the covariant derivative associated with the metric gμνg_{\mu\nu}, ensuring that the energy-momentum flux is locally conserved.