A simple theorem to generate exact black-hole solutions

Under certain conditions imposed on the energy-momentum tensor, a theorem that characterizes a two-parameter family of static and spherically symmetric solutions to Einsteinʹs field equations (black holes) is proved. A discussion on the asymptotics, regularity and the energy conditions is provided. Examples that include the best known exact solutions within these symmetries are considered. A trivial extension of the theorem includes the cosmological constant ab initio, providing then a three-parameter family of solutions.