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Evaluation of circular orbits and innermost stable circular orbits of neutral and charged particles around black holes

Eahsaan Nazir Najar, Raja Nisar Ali, Yasmeena Mushtaq, Imtiyaz Ahmad Bhat

Abstract

In this paper we study the effective gravitational potential of Schwarzschild, Kerr, Reissner-Nordström and Kerr-Newman black holes with the relativistic corrections to evaluate the circular orbits and the Innermost Stable Circular Orbits (ISCOs), a purely relativistic phenomenon, of neutral and charged particles in the vicinity of these spacetimes. We study the circular orbits and ISCOs of black holes mathematically and graphically. Moreover, the astrophysical properties of ISCO are also dealt with. We find that the particle entering the ISCO loses a certain amount of energy, in different spacetimes, by gravitational radiative processes, before finally spiraling into ISCO. The electromagnetic effects of different spacetimes show how the charges sharpen the radius of the circular orbits, and the increasing product of particle and black hole charge increases the radius of the ISCO. Most importantly, the effective potential of the most general spacetime, as predicted by the no-hair conjecture, has been derived.

Evaluation of circular orbits and innermost stable circular orbits of neutral and charged particles around black holes

Abstract

In this paper we study the effective gravitational potential of Schwarzschild, Kerr, Reissner-Nordström and Kerr-Newman black holes with the relativistic corrections to evaluate the circular orbits and the Innermost Stable Circular Orbits (ISCOs), a purely relativistic phenomenon, of neutral and charged particles in the vicinity of these spacetimes. We study the circular orbits and ISCOs of black holes mathematically and graphically. Moreover, the astrophysical properties of ISCO are also dealt with. We find that the particle entering the ISCO loses a certain amount of energy, in different spacetimes, by gravitational radiative processes, before finally spiraling into ISCO. The electromagnetic effects of different spacetimes show how the charges sharpen the radius of the circular orbits, and the increasing product of particle and black hole charge increases the radius of the ISCO. Most importantly, the effective potential of the most general spacetime, as predicted by the no-hair conjecture, has been derived.
Paper Structure (13 sections, 111 equations, 17 figures)

This paper contains 13 sections, 111 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Schwarzschild black hole
  3. Circular orbits of gravitating neutral particles in Schwarzschild black hole
  4. ISCO of charged particles in Schwarzschild black hole
  5. Kerr Black Hole
  6. Circular orbits of gravitating neutral particles in Kerr field
  7. ISCO of charged particles in Kerr black hole
  8. Reissner-Nordström black hole
  9. Circular orbits of gravitating neutral particles in Reissner-Nordström black hole
  10. ISCO of charged particles in Reissner-Nordström black hole
  11. Kerr-Newman Black Hole
  12. Circular orbits of gravitating neutral particles in Kerr-Newman black hole
  13. Conclusion

Figures (17)

  • Figure 1: Variation of potential energy with radius in a Schwarzschild spacetime.
  • Figure 2: Variation of : $r_{\mathcal{ISCO}}/M$ w.r.t. $q/M$ (Top), $\mathcal{E}_{\mathcal{ISCO}}$ w.r.t. $q/M$ (Center) and $\mathcal{L}_{\mathcal{ISCO}}/M$ w.r.t. $q/M$ (Bottom).
  • Figure 3: Variation of : radius $r_{\mathcal{ISCO}}/M$ w.r.t. magnetic parameter $bM$ (Top), specific energy $\mathcal{E}_{0}$ w.r.t. $bM$ (Center) and specific angular momentum $\mathcal{L}_{0}/M$ w.r.t. $bM$ (Bottom).
  • Figure 4: The $r_{\mathcal{ISCO}}/M$ versus $q/M$ for selected values of b for weak (Top) and strong magnetic field (Bottom).
  • Figure 5: Variation of effective potential of Kerr black hole with $r$ for different values of $a$ with $\mathcal{E}=0.5$ and (Top) and $\mathcal{E}=1$ (Bottom).
  • ...and 12 more figures