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Motions of spinning particles and chaos bound in Reissner-Nordström spacetime

Chuang Yang, Deyou Chen, Yongtao Liu

Abstract

In this paper, we investigate Lyapunov exponents of classical chaos of spinning particles orbiting a Reissner-Nordström black hole and examine whether the values of the exponents exceed the chaos bound. For the neutral particle, when its spin magnitude surpasses a specific threshold, the value of the exponent exceeds the surface gravity, resulting in a violation. Given a fixed total angular momentum of the particle, its spin direction opposite to the angular momentum direction leads to a greater exponent value than when the two directions are aligned. For the charged particle, taking into account the influence of the electromagnetic force, we find that, for relatively large angular momenta, although the electromagnetic force does not change the trend of the exponent's variation with respect to spin and angular momentum and only modifies the specific values of the exponent, it still leads to violations of the bound. Therefore, the chaos bound is violated in the spinor field.

Motions of spinning particles and chaos bound in Reissner-Nordström spacetime

Abstract

In this paper, we investigate Lyapunov exponents of classical chaos of spinning particles orbiting a Reissner-Nordström black hole and examine whether the values of the exponents exceed the chaos bound. For the neutral particle, when its spin magnitude surpasses a specific threshold, the value of the exponent exceeds the surface gravity, resulting in a violation. Given a fixed total angular momentum of the particle, its spin direction opposite to the angular momentum direction leads to a greater exponent value than when the two directions are aligned. For the charged particle, taking into account the influence of the electromagnetic force, we find that, for relatively large angular momenta, although the electromagnetic force does not change the trend of the exponent's variation with respect to spin and angular momentum and only modifies the specific values of the exponent, it still leads to violations of the bound. Therefore, the chaos bound is violated in the spinor field.
Paper Structure (9 sections, 26 equations, 11 figures)

This paper contains 9 sections, 26 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Motions of spinning particles around RN BH
  3. Review of MPD equations
  4. Motions of spinning particles
  5. LE and chaos bound
  6. LE
  7. Neutral particle
  8. Charged particle
  9. Conclusions and discussions

Figures (11)

  • Figure 1:
  • Figure 2:
  • Figure 4: Curves show the variation of the effective potential of the neutral particle with its radius, calculated with $L=10.00$.
  • Figure 5:
  • Figure 7:
  • ...and 6 more figures