Exact solutions for spherical gravitational collapse around a black hole: the effect of tangential pressure

  • Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact solutions have three qualitatively different outcomes. For positive tangential pressure, the shell around a black hole may eventually collapse onto the black hole, or expand to infinity, or have a static but unstable solution, depending on the combination of black hole mass, mass of the shell and the pressure parameter. For vanishing or negative pressure, the shell will collapse onto the black hole. For all eventually collapsing solutions, the shell will cross the event horizon, instead of accumulating outside theeventhorizon, even if clocked by a distant stationary observer.
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Sheng-Xian Zhao and Shuang-Nan Zhang. Exact solutions for spherical gravitational collapse around a black hole: the effect of tangential pressure[J]. Chinese Physics C, 2018, 42(8): 085101. doi: 10.1088/1674-1137/42/8/085101
Sheng-Xian Zhao and Shuang-Nan Zhang. Exact solutions for spherical gravitational collapse around a black hole: the effect of tangential pressure[J]. Chinese Physics C, 2018, 42(8): 085101.  doi: 10.1088/1674-1137/42/8/085101 shu
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Received: 2018-03-28
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    Supported by National Natural Science Foundation of China (11373036, 11133002), the National Program on Key Research and Development Project (2016YFA0400802) and the Key Research Program of Frontier Sciences, CAS, (QYZDY-SSW-SLH008)

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Exact solutions for spherical gravitational collapse around a black hole: the effect of tangential pressure

  • 1. Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Beijing 100049, China
  • 4. University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:  Supported by National Natural Science Foundation of China (11373036, 11133002), the National Program on Key Research and Development Project (2016YFA0400802) and the Key Research Program of Frontier Sciences, CAS, (QYZDY-SSW-SLH008)

Abstract: Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact solutions have three qualitatively different outcomes. For positive tangential pressure, the shell around a black hole may eventually collapse onto the black hole, or expand to infinity, or have a static but unstable solution, depending on the combination of black hole mass, mass of the shell and the pressure parameter. For vanishing or negative pressure, the shell will collapse onto the black hole. For all eventually collapsing solutions, the shell will cross the event horizon, instead of accumulating outside theeventhorizon, even if clocked by a distant stationary observer.

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