Spacetime and Geometry · Problem 6.1

Perturbation Theory and Gravitational Radiation — Sean Carroll

Physics — General Relativity · einstein-maxwell-extremal-black-holes

Problem

Show that the coupled Einstein--Maxwell equations can be simultaneously solved by the metric (6.62) and the electrostatic potential (6.67) if

H(\vec{x})

obeys Laplace's equation,

\nabla^2 H = 0. \tag{6.120}