Geometrical theories of gravitation with short-range forces

Abstract

Earlier geometrical theories of gravitation with short-range forces are analyzed, in view of a more general approach, to compare some of the properties of such theories with general relativity (GR). It is found that neither the scalar-tensor nor the fourth-order theories of gravity share with GR the interesting property that the binding energy of a gravitating system may be attributed to the loss of energy in packing the matter under its own gravitational field. This general approach, in the form of a GR field equation with an effective energy-momentum tensor is used to construct a constant-density, spherically-symmetric star model, via a heuristic argument, as a perturbation of the corresponding model in GR to study the modifications to the limiting gravitational mass. The application of the present study to other problems of physical interest is briefly mentioned.