Conceptual

Stress Energy Tensor and Einstein's Field Equations in General Relativity

The abstract theory centers on General Relativity's formulation where spacetime curvature is dynamically determined by the distribution and flux of energy-momentum via Einstein's Field Equations, governed mathematically by differential geometry and tensor calculus. The core principle asserts that mass-energy equivalence implies intrinsic energy within volume expansion, while stress components such as pressure contribute to geometric deformation analogous to material elasticity but defined on a manifold without fixed metric rigidity. This framework extends beyond local descriptions of gravity into global topological properties, suggesting potential limitations in classical General Relativity regarding the complete characterization of spacetime's non-local structure and singularities through advanced differential topology.