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Reissner-Nordström Metric

The Reissner-Nordström metric is the spherically symmetric metric tensor on a Lorentzian manifold for an electrovacuum with mass m and total charge Q. Its static line element is

ds^2=-f(r)dt^2+f(r)^(-1)dr^2+r^2(dtheta^2+sin^2thetadphi^2),

where f(r)=1-2m/r+Q^2/r^2. For electric and magnetic charges, Q^2=Q_e^2+Q_b^2. When m>|Q|>0, the two horizon radii are

r_+/-=m+/-sqrt(m^2-Q^2).

The exterior has r>r_+, and Q=0 gives the Schwarzschild metric. The charged Penrose inequality compares enclosing area with the outer radius in this model.

See also

Charged Penrose Inequality, Lorentzian Manifold, Schwarzschild Metric

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References

Khuri, M.; Weinstein, G.; and Yamada, S. "Proof of the Riemannian Penrose Inequality with Charge for Multiple Black Holes." J. Diff. Geom. 106, 451-498, 2017. https://doi.org/10.4310/jdg/1500084023.Van de Moortel, M. "The Strong Cosmic Censorship Conjecture." C. R. Mécanique 353, 415-454, 2025. https://doi.org/10.5802/crmeca.271.

Cite this as:

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

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