Which tensor represents matter and energy in Einstein's field equations?

The stress-energy tensor represents matter and energy in Einstein’s field equations. Written as Gμν + Λgμν = κTμν, the equation places spacetime curvature on one side and the distribution of energy, momentum, pressure, and stress on the other.

The tensor is broader than ordinary mass density. Its components describe energy density, energy flow, momentum density, and internal stresses such as pressure and shear. Radiation and electromagnetic fields also contribute, even though they have no rest mass. This is why “matter and energy” is a useful quiz-level description, while “stress-energy-momentum” is the more complete name.

The Einstein tensor is a common mix-up: it describes curvature and belongs on the geometric side of the equation. The Riemann tensor gives the full curvature structure, while the Weyl tensor captures the free, conformal part of curvature. None of those is the source tensor representing material or non-gravitational field content.

Einstein published general relativity’s field equations in 1915. In Newtonian gravity, mass density acts as the source; general relativity replaces that narrower idea with the full stress-energy tensor, allowing pressure and energy transport to gravitate as well.