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The 49 pages that link to Einstein field equations, each with the reason it gives.

• General relativityBroader topic: They state the central relation between geometry and physical sources in general relativity.

• Cosmological constantNarrower topic: The cosmological constant enters these equations as an additional geometric term.

• Cosmological principleNarrower topic: The cosmological equations arise by applying these gravitational laws under symmetry assumptions.

• Metric tensorRelated: They determine how the spacetime metric responds to physical sources.

• Friedmann equationsRelated: Imposing cosmic homogeneity and isotropy on these equations yields the Friedmann equations.

• SpacetimeRelated: They express how matter and energy shape the geometry of spacetime.

• Covariant derivativeBroader topic: Their geometric terms are built from curvature defined through covariant differentiation.

• Riemann curvature tensorRelated: Their geometric side is built from contractions of the Riemann tensor.

• Gravitational constantRelated: G sets the coupling between matter-energy and spacetime curvature.

• Cosmological constant problemRelated: They show how vacuum energy can contribute to cosmic curvature.

• Stress–energy tensorRelated: The stress–energy tensor is the source term on their matter side.

• Mercury's perihelion precessionNarrower topic: Einstein derived Mercury’s anomalous advance from his new gravitational field equations.

• Schwarzschild metricNarrower topic: The Schwarzschild metric solves these equations in the vacuum region outside the mass.

• Christoffel symbolsBroader topic: Their curvature terms are often evaluated from Christoffel symbols in a chosen chart.

• Gravitational time dilationNarrower topic: They provide the framework in which gravitational fields determine spacetime geometry and clock rates.

• Kerr metricNarrower topic: The Kerr metric is an exact vacuum solution of these equations.

• Alexander FriedmannBroader topic: Friedmann solved these equations under assumptions suited to cosmology.

• Hyperbolic partial differential equationRelated: After gauge fixing, their evolution formulations have hyperbolic structure.

• GravitationBroader topic: They express how gravitation responds to its sources in general relativity.

• Classical field theoryBroader topic: They govern the evolution and sourcing of the gravitational field in general relativity.

• Mach's principleRelated: They connect matter and geometry, but do not make every solution's inertia depend on all cosmic matter.

• Modified gravityCompared with: Modified-gravity theories alter these equations or their underlying assumptions.

• Tullio Levi-CivitaBroader topic: Levi-Civita clarified the tensor mathematics behind their geometric side.

• Bianchi identitiesRelated: Their geometric side has zero divergence, requiring compatible conservation of the matter side.

• Big CrunchNarrower topic: Cosmic expansion and contraction emerge from applying these equations to the universe as a whole.

• Kaluza–Klein theoryRelated: Kaluza applied their higher-dimensional form to obtain the gravitational and electromagnetic equations.

• Shapiro time delayNarrower topic: They determine the gravitational geometry from which the signal delay follows.

• Vacuum energyRelated: They connect a uniform vacuum energy density to the curvature and expansion of spacetime.

• General covarianceBroader topic: Their tensor form is unchanged by arbitrary smooth coordinate transformations.

• Gregorio Ricci-CurbastroBroader topic: They demonstrate the physical use of the mathematical framework Ricci-Curbastro helped establish.

• Marcel GrossmannBroader topic: The search for suitable curvature equations was a central mathematical challenge in Einstein and Grossmann’s work.

• Karl SchwarzschildNarrower topic: Their vacuum form is the system Schwarzschild solved exactly.

• Static universeRelated: Einstein used these equations to test whether a matter-filled universe could remain unchanging.

• De Sitter universeRelated: They admit De Sitter spacetime when the cosmological constant is positive and matter is absent.

• Gravitational singularityNarrower topic: Their classical solutions produce the spacetimes in which singularity behavior is analyzed.

• Kerr–Newman metricNarrower topic: Their gravitational part governs the geometry in the solution.

• Penrose–Hawking singularity theoremsNarrower topic: The singularity theorems derive their physical significance from applying geometric reasoning to solutions of these equations.

• Curved spacetimeRelated: They state mathematically how matter and energy shape the curvature.

• Expansion of the UniverseNarrower topic: Cosmological expansion emerged from applying these equations to the universe as a whole.

• History of general relativityBroader topic: Einstein’s 1915 field equations are the central mathematical statement of the theory.

• Positive energy theoremRelated: They connect the matter conditions assumed by the theorem to spacetime geometry.

• Buchdahl's theoremNarrower topic: They supply the gravitational field equations used in the theorem’s proof.

• Geometrized unit systemRelated: Setting constants to one removes conversion factors from their standard form.

• Mathematics of general relativityBroader topic: They are the central equations connecting geometry with gravitating matter.

• Principle of covarianceBroader topic: Their tensor form exemplifies coordinate covariance in a physical theory.

• RelativityBroader topic: They specify how matter and energy determine gravitational geometry.

• Ricci calculusBroader topic: They combine the Ricci tensor, scalar curvature, metric, and stress-energy tensor.

• Rotating black holeNarrower topic: The Kerr solution satisfies these equations in vacuum.

• White holeNarrower topic: White holes arise as mathematical possibilities within solutions to these equations.