{"title":"A Study on Geodesics and Lifespan of the Rindler-Modified Schwarzschild Black Hole. I. Time-Like Geodesics","authors":"T. Huo, C. Liu","doi":"10.1007/s10511-025-09862-5","DOIUrl":null,"url":null,"abstract":"<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>","PeriodicalId":479,"journal":{"name":"Astrophysics","volume":"68 1","pages":"120 - 139"},"PeriodicalIF":0.6000,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Astrophysics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10511-025-09862-5","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
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Abstract
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.
期刊介绍：
Astrophysics (Ap) is a peer-reviewed scientific journal which publishes research in theoretical and observational astrophysics. Founded by V.A.Ambartsumian in 1965 Astrophysics is one of the international astronomy journals. The journal covers space astrophysics, stellar and galactic evolution, solar physics, stellar and planetary atmospheres, interstellar matter. Additional subjects include chemical composition and internal structure of stars, quasars and pulsars, developments in modern cosmology and radiative transfer.
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