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Physical Sciences
Relativity
1915
Research

Einstein Field Equations

Gμν+Λgμν=8πGc4TμνG_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}

Curvature of spacetime is determined by energy and momentum—gravity is geometry.

By Albert Einstein

Physical Sciences
Einstein Field Equations
1915 · Albert Einstein
Human Reviewed
84%

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Five doors into the universe behind this equation. Choose your path.

Story PortalWho discovered this?Discover how Albert Einstein and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — gps.Math PortalWhat does it derive from?Trace the mathematical lineage from einstein mass energy.Future PortalWhere is it going?Quantum gravity
Why it matters: Enabled GPS, gravitational waves, black hole imaging, and modern cosmology.

Discoverers: Albert Einstein (1915)

What does it mean?

Curvature of spacetime is determined by energy and momentum—gravity is geometry.

Why should I care?

Enabled GPS, gravitational waves, black hole imaging, and modern cosmology.

Equation Compass

North — Prerequisites

West — History

East — Applications

South — Derivations

Variables & Units

SymbolNameUnitMeaning
GμνG_μνEinstein tensor—Spacetime curvature
TμνT_μνStress-energy—Matter and energy content
ΛΛCosmological constant—Dark energy term

Worked Example

Schwarzschild solution describes non-rotating black holes.

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Albert EinsteinTensor

Pictures & video

Portrait photograph of Albert Einstein, 1921
Albert Einstein, who published the field equations of general relativity in 1915.Ferdinand Schmutzer / Wikimedia Commons · Public domain

Sources & further reading

Einstein field equations — WikipediaSearch WikipediaSearch Wolfram MathWorldOpen in Wolfram|AlphaWatch explainers on YouTube

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Equation Universe

Einstein Field Equations

Gμν+Λgμν=8πGc4TμνG_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}

Real-world impact

GPS & gravitational waves

Spacetime curvature enables precision navigation and LIGO detections.

Photo: Unsplash — Earth from space

Curvature of spacetime is determined by energy and momentum—gravity is geometry.

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