Reissner–Nordström metric

In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein-Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M.

The metric was discovered by Hans Reissner and Gunnar Nordström.

These four related solutions may be summarized by the following table:

where Q represents the body's electric charge and J represents its spin angular momentum.

In spherical coordinates (t, r, θ, φ), the line element for the Reissner–Nordström metric is

where c is the speed of light, t is the time coordinate (measured by a stationary clock at infinity), r is the radial coordinate, ${\displaystyle \textstyle d\Omega _{(2)}^{2}}$ is a 2-sphere defined by

r_S is the Schwarzschild radius of the body given by

and r_Q is a characteristic length scale given by

Here 1/4πε₀ is Coulomb force constant.

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