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arXiv · 2507.15107

General form for Pseudo-Newtonian Potentials, imitating Schwarzschild geodesics

Itamar Ben Arosh Arad·Reem Sari
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Abstract

We propose a new, general form for a pseudo-Newtonian gravitational potential (PNP), expressed as a series of Paczy\'nski-Wiita-like functions with the addition of increasing negative powers of $r$ with arbitrary coefficients. We present a procedure for determining these coefficients to construct a custom PNP that replicates key features of Schwarzschild geodesics for a test particle near a black hole. As an example, we construct potentials set to reproduce (I) the presence of an innermost stable circular orbit at the $r=6$ (geometric units), with the correct infall velocity for small deviations (on the geodesic universal infall), (II) the periapsis advance at large distances, and (III) the presence of a marginally bound circular orbit with specific angular momentum $L=4$, and the periapsis advance of parabolic orbits close to it. We compare the performance of our examples against the Paczy\'nski-Wiita potential and other existing potentials. Finally, we discuss the limitations and advantages of our formulation.

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Itamar Ben Arosh Arad, Reem Sari. 2025-07-20. General form for Pseudo-Newtonian Potentials, imitating Schwarzschild geodesics. https://doi.org/10.3847/1538-4357%2Fae433f

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