Exact relativistic Newtonian representation of gravitational static spacetime geometries

Abstract

We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, staring directly from a generalized scalar relativistic gravitational action in Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite useful in studying wide range of astrophysical phenomena, especially in strong field gravity.

6 pages, 1 table

References in corpus (5)

• The Confrontation between General Relativity and Experiment
• Pseudo-Newtonian gravitational potential for Schwarzschild-de Sitter spacetimes
• Generalized pseudo-Newtonian potential for studying accretion disk dynamics in off-equatorial planes around rotating black holes: Description of a vector potential
• Newtonian analogue of corresponding spacetime dynamics of rotating black holes: Implication on black hole accretion
• Newtonian analogue of Schwarzschild de-Sitter spacetime: Influence on the local kinematics in galaxies

Cited by in corpus (3)

• Spherical accretion in giant elliptical galaxies: multi-transonicity, shocks, and implications on AGN feedback
• Relativity from the Geometrization of Newtonian Dynamics
• Spherical accretion in the Schwarzschild spacetime in the Newtonian analogous construct