Relativistic Newtonian gravity: an improved version

Abstract

In view of a serious error found in a recent article by Biswas (1988) an improved version of the author's flat spacetime theory of gravitation has been presented. Twofold modifications to Biswas' theory (BT) have been suggested. Firstly, to obtain particle trajectories, instead of using Biswas' noncovariant Hamiltonian formulation, a covariant Lagrangian formulation has been developed to obtain the equation of motion of test objects. Secondly, the nongeneral-relativistic field equations of BT have also been modified. It has been shown that with these changes the present theory when applied to a matter-free spherically symmetric situation, produces correct values for the advance of the perihelion of Mercury's orbit and bending of light near the Sun. The energy integral for a particle trajectory has been calculated. This has been used to obtain the general red shift formula. A brief survey of some other flat spacetime theories of gravitation is also presented, to demonstrate how in spite of its error, BT stands out in sharp contrast in its ability to provide a direction along which a viable relativistic theory of gravitation can be obtained.