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.