CAOSP abstracts, Volume: 53, No.: 2, year: 2023

Abstract: In general relativity, the acceleration of a test particle in the vicinity of a massive object should be calculated by using the equation of geodesic. The specific formula for the acceleration is, however, well-known only in the Schwarzschild coordinates. Here, we present this formula in the frame with the spatial part identical to the common rectangular coordinate frame. The orientation of the acceleration and identification of physical quantities with the general integration constants can better be discerned in the latter. We emphasize that the gravitational acceleration in general relativity, for system of particles being in rest, consists of two terms. The first term is identical with the acceleration derived on the basis of Newton's gravitational law. The second term, having a smaller size above the event horizon, is a repulsive contribution to the total, attractive, gravity. The relativistic formula implies that the gravity should be repulsive below the event horizon, because the second term dominates in this region.