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Retrograde Precession of Relativistic Orbits and the Quest for Charged Black Holes

Parth Bambhaniya, Meet J. Vyas, Pankaj S. Joshi, Elisabete M. de Gouveia Dal Pino

TL;DR

The paper investigates periastron precession of timelike equatorial orbits around charged spacetimes as a test of charged black holes and naked singularities in the Galactic Center. It derives fully relativistic orbit equations for the Reissner-Nordström and Kerr-Newman geometries and solves them numerically, supplemented by low-eccentricity analytic approximations to map precession signs. The key finding is that retrograde (negative) precession can occur for naked-singularity configurations in RN and KN spacetimes, while uncharged Schwarzschild and Kerr spacetimes show prograde precession, indicating a distinct imprint of charge on orbital dynamics. These results suggest that future measurements of S-star trajectories around Sgr A* could help constrain or rule out charged geometries and shed light on the true spacetime geometry of the Galactic Center.

Abstract

The S-stars around the center of the milky way galaxy provide us with detailed information about the nature of the supermassive compact object Sagittarius A* (Sgr A*). In this work, we derive the fully relativistic orbit equations for the case of the Reissner-Nordström (RN) and Kerr-Newman spacetimes. We solve these orbit equations numerically to analyze the periastron shift of relativistic orbits. We show that retrograde precession (or negative precession) of timelike bound orbits is possible in the case of naked singularity arising from these spacetimes. We have then compared our results with the non-charged Schwarzschild and Kerr spacetimes. This theoretical analysis of relativistic orbits would be helpful in either confirming or ruling out such charged black holes and naked singularities through the future trajectories of S-stars and will also help us constrain the geometry of Sgr A*.

Retrograde Precession of Relativistic Orbits and the Quest for Charged Black Holes

TL;DR

The paper investigates periastron precession of timelike equatorial orbits around charged spacetimes as a test of charged black holes and naked singularities in the Galactic Center. It derives fully relativistic orbit equations for the Reissner-Nordström and Kerr-Newman geometries and solves them numerically, supplemented by low-eccentricity analytic approximations to map precession signs. The key finding is that retrograde (negative) precession can occur for naked-singularity configurations in RN and KN spacetimes, while uncharged Schwarzschild and Kerr spacetimes show prograde precession, indicating a distinct imprint of charge on orbital dynamics. These results suggest that future measurements of S-star trajectories around Sgr A* could help constrain or rule out charged geometries and shed light on the true spacetime geometry of the Galactic Center.

Abstract

The S-stars around the center of the milky way galaxy provide us with detailed information about the nature of the supermassive compact object Sagittarius A* (Sgr A*). In this work, we derive the fully relativistic orbit equations for the case of the Reissner-Nordström (RN) and Kerr-Newman spacetimes. We solve these orbit equations numerically to analyze the periastron shift of relativistic orbits. We show that retrograde precession (or negative precession) of timelike bound orbits is possible in the case of naked singularity arising from these spacetimes. We have then compared our results with the non-charged Schwarzschild and Kerr spacetimes. This theoretical analysis of relativistic orbits would be helpful in either confirming or ruling out such charged black holes and naked singularities through the future trajectories of S-stars and will also help us constrain the geometry of Sgr A*.
Paper Structure (11 sections, 45 equations, 8 figures)

This paper contains 11 sections, 45 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Relativistic Orbit Equations in Charged Spacetimes
  3. Orbit equation for RN spacetime
  4. Orbit equation for Kerr-Newman spacetime
  5. An approximate solution of the Orbit Equation for the RN spacetime
  6. An approximate solution of the Orbit Equation for the Kerr-Newman spacetime
  7. Periastron shift comparison with non-charged spacetimes
  8. Discussions and Conclusions
  9. Full Length Equations
  10. Kerr-Newman Orbit Equation
  11. Zeroth and First Order Terms in Kerr-Newman m-plot

Figures (8)

  • Figure 1: Effective potential plot of RN spacetime for $L=3$, $q=2$, $M=1$, $E=-0.02$, and $0 \leq r \leq 50$
  • Figure 2: Relativistic orbits in the Reissner-Nordstrom Spacetime for $L=3$, $q=2$, $M=1$, $E=-0.02$, and $r_{min} = 6.3282$
  • Figure 3: Effective potential of Kerr-Newman spacetime
  • Figure 4: Relativistic orbits in the Kerr-Newman Spacetime for $L=8$, $q=2.5$, $M=1$, $E=-0.005$, $a = 0.8$, and $0 \leq r \leq 300$
  • Figure 5: $m-q$ plot for the RN spacetime solution Eq. (\ref{['m_plot_eq_rn']}) for the parametric range: $M=1$, $~3\leq L\leq 10$, $~0.965\leq e\leq 0.999$.
  • ...and 3 more figures