What is the name of the equations that describe the gravitational field in general relativity?

The equations that describe the gravitational field in general relativity are the Einstein field equations. They connect the geometry, or curvature, of spacetime with matter, energy, momentum, and stress.

Albert Einstein published the equations in 1915, completing the central mathematical framework of general relativity. In their standard form, the left side describes spacetime curvature through the Einstein tensor and cosmological constant, while the right side contains the stress-energy tensor describing physical contents of the universe.

The equations are not simply a formula for gravitational force. Their solutions determine the spacetime metric, which governs how clocks, rulers, light, and freely falling objects behave. They are nonlinear, so exact solutions usually require simplifying assumptions such as spherical symmetry or a weak gravitational field.

Several famous predictions and models arise from these equations, including black holes, gravitational waves, and expanding-universe solutions. Maxwell's equations describe electromagnetism, the Schrödinger equation belongs to quantum mechanics, and the Friedmann equations are specialized cosmological equations derived from the Einstein field equations under assumptions of large-scale uniformity.