The equations of motion in spacetime endowed with stationary metric of general relativity and the equivalent gravitational scalar generalized potential of special relativity

Abstract The gravity in the context of general relativity (GR) as dynamical curvature of spacetime remains a principal impediment not only to its unification with the other fundamental interactions but also to the formulation of quantum gravity. One possible resolution involves considering gravity in the context of special relativity (SR). This paper presents a procedure, which correlates the GR metrics of curved spacetime and the SR gravitational scalar generalized potential. The GR time dilation is the key-point for the correlation of the two gravities, which implies the corresponding SR Lagrangian. Previous papers have already demonstrated the procedure and the results in cases of Friedmann–Lemaitre–Robertson–Walker metric, wormholes with spherical symmetry, and Schwarzschild metric (where not only the gravitational motions (free falls) but also the Gravitational Red Shift in the context of SR are exactly the same as those in the context of GR with stationary metric). This paper analytically derives the general formulae of Equations of Motion in Spacetime endowed with Stationary metric in the context of GR and the ones in the context of SR, proving that they are exactly the same. Finally, it presents the case studies of gravitational motions around Schwarzschild blackhole, Kerr rotating blackhole and Standard Ellis–Bronnikov wormhole. Thus, it is shown that these motions have an equivalent SR viewpoint.