Entropic gravity versus gravitational pseudotensors in static spherically symmetric spacetimes

Abstract

We present some well-known energy-momentum complexes and evaluate the gravitational energy associated with static spherically symmetric spacetimes. In fact, the energy distribution of the aforementioned gravitational background that is contained in a two-sphere of radius $r$ shows that a test particle situated at a finite distance $r$ experiences the gravitational field of the effective gravitational mass. In addition, we apply Verlinde's entropic gravity to find the emergent gravitational energy on static spherically symmetric screens. In this setup, we find that the energy distribution in the prescription of M{\o}ller is similar to the energy derived from the emergent gravity, while other prescriptions give the different results. This result may confirm the argument of Lessner who argues that M{\o}ller's definition of energy is a powerful concept of energy in General Relativity.