Quasi-local photon surfaces in general spherically symmetric spacetimes
Based on the geometry of the codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one provided by Claudel, Virbhadra, and Ellis but without referencing any u...
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| Published in | The European physical journal. C, Particles and fields Vol. 81; no. 8; pp. 1 - 16 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Springer Berlin Heidelberg
01.08.2021
Springer Springer Nature B.V SpringerOpen |
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| Abstract | Based on the geometry of the codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one provided by Claudel, Virbhadra, and Ellis but without referencing any umbilical hypersurface in the spacetime. The new definition effectively excludes the photon surface in spacetime without gravity. The application of the definition to the Lemaître–Tolman–Bondi (LTB) model of gravitational collapse reduces to a second order differential equation problem. We find that the energy balance on the boundary of the dust ball can provide one of the appropriate boundary conditions to this equation. Based on this crucial investigation, we find an analytic photon surface solution in the Oppenheimer–Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of the gravitational field of the system. |
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| AbstractList | Based on the geometry of the codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one provided by Claudel, Virbhadra, and Ellis but without referencing any umbilical hypersurface in the spacetime. The new definition effectively excludes the photon surface in spacetime without gravity. The application of the definition to the Lemaître-Tolman-Bondi (LTB) model of gravitational collapse reduces to a second order differential equation problem. We find that the energy balance on the boundary of the dust ball can provide one of the appropriate boundary conditions to this equation. Based on this crucial investigation, we find an analytic photon surface solution in the Oppenheimer-Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of the gravitational field of the system. Abstract Based on the geometry of the codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a photon surface. This new definition is the generalization of the one provided by Claudel, Virbhadra, and Ellis but without referencing any umbilical hypersurface in the spacetime. The new definition effectively excludes the photon surface in spacetime without gravity. The application of the definition to the Lemaître–Tolman–Bondi (LTB) model of gravitational collapse reduces to a second order differential equation problem. We find that the energy balance on the boundary of the dust ball can provide one of the appropriate boundary conditions to this equation. Based on this crucial investigation, we find an analytic photon surface solution in the Oppenheimer–Snyder (OS) model and reasonable numerical solutions for the marginally bounded collapse in the LTB model. Interestingly, in the OS model, we find that the time difference between the occurrence of the photon surface and the event horizon is mainly determined by the total mass of the system but not the size or the strength of the gravitational field of the system. |
| ArticleNumber | 714 |
| Audience | Academic |
| Author | Song, Yong Cao, Li-Ming |
| Author_xml | – sequence: 1 givenname: Li-Ming surname: Cao fullname: Cao, Li-Ming email: caolm@ustc.edu.cn organization: Interdisciplinary Center for Theoretical Study, University of Science and Technology of China – sequence: 2 givenname: Yong surname: Song fullname: Song, Yong organization: Interdisciplinary Center for Theoretical Study, University of Science and Technology of China |
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| Cites_doi | 10.4310/CAG.2017.v25.n2.a2 10.1088/0264-9381/13/3/019 10.1088/0264-9381/3/4/007 10.1007/JHEP03(2011)112 10.1088/0264-9381/17/2/101 10.1103/PhysRevD.19.2239 10.1093/acprof:oso/9780198528906.001.0001 10.12942/lrr-2004-10 10.1103/PhysRevD.99.084043 10.1088/0264-9381/22/21/001 10.1103/PhysRevD.77.024003 10.1103/PhysRevD.86.063010 10.1103/PhysRevD.100.044057 10.1023/A:1015384604371 10.1103/PhysRevD.74.044027 10.1103/PhysRevD.100.104005 10.1103/PhysRevD.96.024039 10.1103/PhysRevD.92.044035 10.1007/s10714-014-1818-8 10.1007/978-3-319-30066-5 10.1103/PhysRevD.77.064031 10.1103/PhysRevD.49.6467 10.1088/0264-9381/13/11/019 10.1103/PhysRevD.22.1233 10.1088/0264-9381/33/7/075006 10.1093/mnras/sty2624 10.1007/s10714-018-2361-9 10.1063/1.1308507 10.1140/epjc/s10052-020-8070-z 10.1103/PhysRevD.100.044058 10.1088/0264-9381/31/23/235008 10.1103/PhysRevD.99.104080 10.1088/0264-9381/32/16/165021 10.1103/PhysRevD.95.044047 10.1139/p11-032 10.1088/0004-637X/777/2/170 10.1103/PhysRevD.65.103004 10.1088/0264-9381/32/24/247001 10.7208/chicago/9780226870373.001.0001 |
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| Snippet | Based on the geometry of the codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as well as a... Abstract Based on the geometry of the codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition of a photon sphere as... |
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| Title | Quasi-local photon surfaces in general spherically symmetric spacetimes |
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