Where is the energy stored in a gravitational field?

Abstract

The meaning and location of energy density in gravitational fields is considered in analogy with the energy density in electrostatic fields. The fact that energy density of gravitational fields acts as a source of gravitation makes the localization, in principle, an observable possibility. A nonlinear Newtonian theory of gravity is explored, and the sensitivity of the predicted perihelion precession to the location of energy density is discussed. Problems associated with identification of gravitational energy density in general relativity are pointed out, together with the similar effects generated by gravitational stresses. Comparison with the nonlinear Newtonian theory allows one to determine the various effects which contribute to the general relativistic perihelion precession.