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Schwarzschild Metric

The Schwarzschild metric is a spherically symmetric metric tensor on a Lorentzian manifold, with vanishing Ricci curvature tensor (Ricci-flat) and mass parameter m. In its static exterior coordinates it is

ds^2=-(1-(2m)/r)dt^2+(1-(2m)/r)^(-1)dr^2+r^2(dtheta^2+sin^2thetadphi^2).

For m>0, the static exterior is r>2m. The apparent singularity at r=2m is a coordinate singularity removable by a different coordinate chart (Visser 2008). Schwarzschild spatial slices are the equality models for the neutral Penrose inequality.

See also

Kerr Metric, Lorentzian Manifold, Penrose Inequality, Riemannian Penrose Inequality

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References

Visser, M. "The Kerr Spacetime: A Brief Introduction." 15 Jan 2008. https://arxiv.org/abs/0706.0622v3.

Cite this as:

Weisstein, Eric W. "Schwarzschild Metric." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchwarzschildMetric.html

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