# Exact relativistic Newtonian representation of gravitational static spacetime geometries

## TL;DR

This paper develops a relativistic Newtonian-like potential that exactly replicates the geodesic motion and gravitational effects of any static spherical symmetric spacetime, aiding astrophysical studies in strong gravity regimes.

## Contribution

It introduces a scalar relativistic potential derived from a generalized action that reproduces the full relativistic gravitational features of static spherical spacetimes.

## Key findings

- Potential reproduces all tested weak-field gravitational effects
- Provides a tool for studying strong field astrophysical phenomena
- Exact correspondence with relativistic geodesic equations

## 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.