Schwarzschild metric

The Schwarzschild metric is an exact solution of Einstein’s field equations describing spacetime outside a spherical, nonrotating mass, with no electric charge.

Schwarzschild coordinates: A time and radial coordinate system in which the Schwarzschild metric has a simple diagonal form. These coordinates express the metric and make its horizon-related coordinate singularity explicit.
Einstein field equations: Equations relating spacetime curvature to the distribution of matter and energy. The Schwarzschild metric solves these equations in the vacuum region outside the mass.
Mercury's perihelion precession: The gradual rotation of Mercury's closest-approach direction around the Sun. The Schwarzschild geometry accounts for the relativistic part of Mercury's orbital precession.
Kerr metric: An exact vacuum solution describing the exterior spacetime of a rotating, uncharged mass. Unlike Schwarzschild, it includes angular momentum and describes rotating black holes.
Event horizon: A boundary beyond which no future-directed signal can reach distant observers. At the Schwarzschild radius, the metric's coordinate description marks the horizon of a black hole.
Vacuum solution: A solution of gravitational field equations in a region where the stress-energy tensor vanishes. The metric describes the exterior vacuum, not the matter inside the spherical body.
Gravitational lens: A massive object whose gravity bends light from a more distant source. Light paths in the Schwarzschild geometry provide a basic model of gravitational lensing.
Reissner–Nordström metric: An exact solution describing the exterior spacetime of a spherical, charged, nonrotating mass. It adds electric charge, absent from the Schwarzschild solution.
Gravitational time dilation: The difference in elapsed time between clocks at different gravitational potentials. The metric predicts that stationary clocks nearer the mass tick more slowly.
Spherical symmetry: Invariance under rotations about a central point. This symmetry sharply restricts the form of the exterior spacetime geometry.

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