Schwarzschild metric fixes the Klein-Gordon single-scalar field to act as cosmological constant

Abstract

We consider the field equations of General Relativity with the Klein-Gordon (single-scalar) field acting as the source in the stress-energy tensor. We set the space-time to be of spherically symmetric and static features of Schwarzschild metric, and take the scalar field as a classical static field. Solutions fix the field as constant and lead to an associated result that the scalar field acts as a cosmological constant.