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<p>We study the time-like geodesics in the spacetime of the Rindler-modified Schwarzschild black hole (RMSBH) with a cosmological constant. We find that for massive particles, whether undergoing radial motion or orbital motion, are unable to escape the black hole. Meanwhile, at larger orbital radii, the cosmological constant significantly modifies the proper velocity of particles. Additionally, in the case where Λ = 0, we have presented a special solution: if the particle is located on a specific circular orbit, its proper velocity will remain unaffected by the Rindler acceleration. Furthermore, we discuss the stability of circular orbits by employing the Lyapunov exponent, and draw the dividing line between stable and unstable circular orbits.</p>

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A Study on Geodesics and Lifespan of the Rindler-Modified Schwarzschild Black Hole. I. Time-Like Geodesics

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • T. Huo,
  • C. Liu

摘要

We study the time-like geodesics in the spacetime of the Rindler-modified Schwarzschild black hole (RMSBH) with a cosmological constant. We find that for massive particles, whether undergoing radial motion or orbital motion, are unable to escape the black hole. Meanwhile, at larger orbital radii, the cosmological constant significantly modifies the proper velocity of particles. Additionally, in the case where Λ = 0, we have presented a special solution: if the particle is located on a specific circular orbit, its proper velocity will remain unaffected by the Rindler acceleration. Furthermore, we discuss the stability of circular orbits by employing the Lyapunov exponent, and draw the dividing line between stable and unstable circular orbits.