Home Wikituition Browse all terms Categories
Random term
Astrophysics, Cosmology & Relativity

Einstein Field Equations

The set of 10 non-linear partial differential equations in general relativity relating spacetime curvature (Ricci tensor R_μν) to stress-energy-momentum T_μν.

Governing formula R_μν - ½ R g_μν + Λ g_μν = (8 π G / c⁴) T_μν
SI unit Non-linear 4D Tensor Equations

In depth

John Wheeler summarized: 'Spacetime tells matter how to move; matter tells spacetime how to curve.' Solutions yield Schwarzschild black holes, Friedmann-Lemaître-Robertson-Walker expanding universe models, and gravitational waves.

Examples in the real world

Solving Einstein field equations for expanding FLRW metric space to derive Friedmann cosmological expansion equations.