Geodesic motion of test particles around the scalar hairy black holes with asymmetric vacua.

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Title: Geodesic motion of test particles around the scalar hairy black holes with asymmetric vacua.
Authors: Chen, Hongyu1 (AUTHOR) hongyuchen0306@qq.com, Fan, Wei1 (AUTHOR) fanwei@just.edu.cn, Chew, Xiao Yan1 (AUTHOR) xiao.yan.chew@just.edu.cn
Source: European Physical Journal C -- Particles & Fields. Mar2025, Vol. 85 Issue 3, p1-10. 10p.
Subjects: Schwarzschild black holes, Geodesic motion, Pseudopotential method, Black holes, Geodesic equation
Abstract: An asymptotically flat hairy black hole (HBH) can exhibit distinct characteristics when compared to the Schwarzschild black hole, due to the evasion of no-hair theorem by minimally coupling the Einstein gravity with a scalar potential which possesses asymmetric vacua, i.e, a false vacuum (ϕ = 0) and a true vacuum (ϕ = ϕ 1) . In this paper, we investigate the geodesic motion of both massive test particles and photons in the vicinity of HBH with ϕ 1 = 0.5 and ϕ 1 = 1.0 by analyzing their effective potentials derived from the geodesic equation. By fixing ϕ 1 , the effective potential of a massive test particle increases monotonically when its angular momentum L is very small. When L increases to a critical value, the effective potential possesses an inflection point which is known as the innermost stable circular orbit (ISCO), where the test particle can still remain stable in a circular orbit with a minimal radius without being absorbed by the HBH or fleeing to infinity. Beyond the critical value of L, the effective potential possesses a local minimum and a local maximum, indicating the existence of unstable and stable circular orbits, respectively. Moreover, the HBH possesses an unstable photon sphere but its location slightly deviates from the Schwarzschild black hole. The trajectories of null geodesics in the vicinity of HBH can also be classified into three types, which are the direct, lensing, and photon sphere, based on the deflection angle of light, but the values of impact parameters can vary significantly than the Schwarzschild black hole. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Geodesic motion of test particles around the scalar hairy black holes with asymmetric vacua.
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  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Hongyu%22">Chen, Hongyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hongyuchen0306@qq.com</i><br /><searchLink fieldCode="AR" term="%22Fan%2C+Wei%22">Fan, Wei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fanwei@just.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Chew%2C+Xiao+Yan%22">Chew, Xiao Yan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xiao.yan.chew@just.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Mar2025, Vol. 85 Issue 3, p1-10. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Schwarzschild+black+holes%22">Schwarzschild black holes</searchLink><br /><searchLink fieldCode="DE" term="%22Geodesic+motion%22">Geodesic motion</searchLink><br /><searchLink fieldCode="DE" term="%22Pseudopotential+method%22">Pseudopotential method</searchLink><br /><searchLink fieldCode="DE" term="%22Black+holes%22">Black holes</searchLink><br /><searchLink fieldCode="DE" term="%22Geodesic+equation%22">Geodesic equation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: An asymptotically flat hairy black hole (HBH) can exhibit distinct characteristics when compared to the Schwarzschild black hole, due to the evasion of no-hair theorem by minimally coupling the Einstein gravity with a scalar potential which possesses asymmetric vacua, i.e, a false vacuum (ϕ = 0) and a true vacuum (ϕ = ϕ 1) . In this paper, we investigate the geodesic motion of both massive test particles and photons in the vicinity of HBH with ϕ 1 = 0.5 and ϕ 1 = 1.0 by analyzing their effective potentials derived from the geodesic equation. By fixing ϕ 1 , the effective potential of a massive test particle increases monotonically when its angular momentum L is very small. When L increases to a critical value, the effective potential possesses an inflection point which is known as the innermost stable circular orbit (ISCO), where the test particle can still remain stable in a circular orbit with a minimal radius without being absorbed by the HBH or fleeing to infinity. Beyond the critical value of L, the effective potential possesses a local minimum and a local maximum, indicating the existence of unstable and stable circular orbits, respectively. Moreover, the HBH possesses an unstable photon sphere but its location slightly deviates from the Schwarzschild black hole. The trajectories of null geodesics in the vicinity of HBH can also be classified into three types, which are the direct, lensing, and photon sphere, based on the deflection angle of light, but the values of impact parameters can vary significantly than the Schwarzschild black hole. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1140/epjc/s10052-025-13948-x
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      – Code: eng
        Text: English
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        PageCount: 10
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      – SubjectFull: Schwarzschild black holes
        Type: general
      – SubjectFull: Geodesic motion
        Type: general
      – SubjectFull: Pseudopotential method
        Type: general
      – SubjectFull: Black holes
        Type: general
      – SubjectFull: Geodesic equation
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      – TitleFull: Geodesic motion of test particles around the scalar hairy black holes with asymmetric vacua.
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            NameFull: Chen, Hongyu
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            NameFull: Fan, Wei
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            NameFull: Chew, Xiao Yan
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              M: 03
              Text: Mar2025
              Type: published
              Y: 2025
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