General form for Pseudo-Newtonian Potentials, imitating Schwarzschild geodesics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908872702164992 |
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| author | Arad, Itamar Ben Arosh Sari, Reem |
| author_facet | Arad, Itamar Ben Arosh Sari, Reem |
| contents | We propose a new, general form for a pseudo-Newtonian gravitational potential (PNP), expressed as a series of Paczyński-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 Paczyński-Wiita potential and other existing potentials. Finally, we discuss the limitations and advantages of our formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General form for Pseudo-Newtonian Potentials, imitating Schwarzschild geodesics Arad, Itamar Ben Arosh Sari, Reem General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena We propose a new, general form for a pseudo-Newtonian gravitational potential (PNP), expressed as a series of Paczyński-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 Paczyński-Wiita potential and other existing potentials. Finally, we discuss the limitations and advantages of our formulation. |
| title | General form for Pseudo-Newtonian Potentials, imitating Schwarzschild geodesics |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2507.15107 |