Equations · equation

Einstein Field Equations

General Relativity · 1915

Equation: G_μν + Λg_μν = (8πG/c⁴)·T_μν
Field: General Relativity
Named After: Albert Einstein
Year: 1915

Symbols

G_μν the Einstein tensor — the Ricci curvature with its trace removed, which is the one combination whose divergence vanishes identically, and therefore the only one that can sit opposite a conserved T_μν · Λ the cosmological constant · g_μν the metric · T_μν the stress-energy tensor: energy density, momentum flow and pressure

Significance

Matter tells spacetime how to curve; curved spacetime tells matter how to move. Black holes, gravitational waves, and the expanding universe live here.

Timeline

Theories

Quantum Gravity Dark Energy Loop Quantum Gravity Black Hole Thermodynamics General Relativity

Related

Schwarzschild Radius Law of Universal Gravitation Geodesic Equation First Friedmann Equation Mass–Energy Equivalence Euler–Lagrange Equation FLRW Metric

Constants

Pi Newtonian constant of gravitation Speed of light in vacuum

Requires

Riemann Curvature Tensor Einstein–Hilbert Action

Required By

First Friedmann Equation Second Friedmann Equation Gravitational Time Dilation Schwarzschild Radius

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From the Equations database in Notion, last edited 2026-08-26. This page is the row, rendered by the build; nothing on it is written by hand.