Stress–energy tensor

The stress–energy tensor represents energy density, momentum density, energy and momentum flow, and mechanical stresses in spacetime. In general relativity, it describes matter and nongravitational fields that influence spacetime curvature.

Energy density: Energy per unit volume in a specified reference frame. The time-time component gives energy density for an observer’s frame.
Special relativity: The theory of space, time, and motion in inertial frames when gravity is neglected. It establishes the spacetime framework in which energy and momentum combine.
Einstein field equations: Equations relating spacetime curvature to the distribution of energy and momentum. The stress–energy tensor is the source term on their matter side.
Canonical stress–energy tensor: A tensor derived from a field’s Lagrangian using spacetime translation symmetry. It may be nonsymmetric, unlike the symmetric tensor commonly used in general relativity.
Momentum density: Momentum per unit volume in a specified reference frame. Time-space components encode momentum density and energy flux.
Tensor: A geometric object whose components transform consistently under changes of coordinates. Tensor transformation rules make its physical content independent of coordinates.
Einstein tensor: A curvature tensor whose covariant divergence vanishes and which appears in Einstein’s field equations. It is matched to the stress–energy tensor to determine gravitational geometry.
Belinfante–Rosenfeld stress–energy tensor: A symmetrized stress–energy tensor formed by improving the canonical tensor with spin-current terms. It illustrates how distinct field-theory constructions can yield a suitable gravitational source.
Stress (physics): Internal force per unit area, represented by a tensor in a continuum. Space-space components represent pressure and shear stress.
Four-momentum: The relativistic four-vector combining energy and three-momentum. The tensor extends four-momentum from a particle to a local distribution and flow.

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