On the energy of Schwarzschild spacetime with the post-Newtonian approximation

Abstract

With the post-Newtonian approximation, the energy of Schwarzschild spacetime in the Weinberg prescription is obtained. The energy for the first post-Newtonian approximation [Formula: see text] gives the Newtonian treatment of Schwarzschild spacetime. However, for the second post-Newtonian approximation, the energy is shown that [Formula: see text] adds extra terms [Formula: see text] which consist of the energy stored in the configuration [Formula: see text], in the gravitational field [Formula: see text], and a term of surface integral. These extra terms give post-Newtonian corrections to the Newtonian treatment.