Global existence of classical static solutions of four dimensional Einstein–Klein–Gordon system

Abstract

In this paper, we prove the global existence of classical static solutions of Einstein’s gravitational theory coupled to a real scalar field where spacetime admits spherically symmetry. The equations of motions can then be reduced into a single first-order integro-differential equation. First, we obtain the decay estimates of the solutions. Then, to prove the global existence, we use the contraction mapping theorem in the appropriate function spaces.