Stress-energy tensor
The stress-energy tensor Tμν is the source term in the Einstein field equations, encoding the density and flux of energy and momentum at each point in spacetime. Unlike the Newtonian gravitational potential, which responds only to mass density, the stress-energy tensor couples gravity to all forms of energy — mass, kinetic energy, pressure, stress, and even the energy of the vacuum itself. The 00 component is energy density; the 0i components are momentum density; and the ij components are the stresses (pressures and shears) in the matter distribution.
The stress-energy tensor is constrained by local conservation laws expressed as ∇μTμν = 0, a tensor equation that generalizes the continuity equation and Newton's third law to curved spacetime. This conservation law is not imposed externally; it is a mathematical consequence of the Einstein equations through the Bianchi identities. The geometry constrains the matter, and the matter constrains the geometry — neither is prior.
In the standard model of cosmology, the stress-energy tensor is dominated by three components: matter (pressureless dust, like galaxies), radiation (relativistic particles, like photons and neutrinos), and dark energy (a component with negative pressure that drives cosmic acceleration). The relative proportions of these components evolve as the universe expands, and their equation of state — the relation between pressure and energy density — determines the future geometry of spacetime.
The stress-energy tensor reveals that general relativity does not treat gravity as a property of mass alone. A stiff spring under compression contributes to spacetime curvature. A magnetic field curves space. The vacuum itself — empty space — curves space if it carries energy. The Newtonian intuition that gravity is what heavy things do is not wrong; it is merely a special case of a far more general principle: that anything that carries energy participates in the geometry of the universe.