Quasi-local photon surfaces in general spherically symmetric spacetimes

Abstract

Based on the geometry of the codimension-2 surface in a 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 by Claudel, Virbhadra, and Ellis but without reference to any umbilical hypersurface in the spacetime. The new definition effectively rules out the photon surface which has noting to do with gravity. The application of the definition to the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse reduces to a problem of a second order differential equation. We find that the energy balance on the boundary of the dust ball can provide one appropriate boundary condition to this equation. Based on this key 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 gravitational field of the system.

arXiv commentrevtex, 19 pages, 10 figures; v3, references added, one definition is improved, typos are corrected

References in corpus (31)

• Isolated and dynamical horizons and their applications
• General Laws of Black-Hole Dynamics
• The geometry of photon surfaces
• Shadows and strong gravitational lensing: a brief review
• Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• Shadows of spherically symmetric black holes and naked singularities
• Photon Rings around Kerr and Kerr-like Black Holes
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• The Final Fate of Spherical Inhomogeneous Dust Collapse
• Understanding photon sphere and black hole shadow in dynamically evolving spacetimes
• Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
• Frame dragging and bending of Light in Kerr and Kerr-(anti) de Sitter spacetimes
• Can strong gravitational lensing distinguish naked singularities from black holes?
• Gravitational lensing and frame dragging of light in the Kerr-Newman and the Kerr-Newman-(anti) de Sitter black hole spacetimes
• The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity
• Uniqueness of photon spheres in electro-vacuum spacetimes
• Shadow of a naked singularity
• Particle and photon orbits in McVittie spacetimes
• Uniqueness of the static Einstein-Maxwell spacetimes with a photon sphere
• Completing characterization of photon orbits in Kerr and Kerr-Newman metrics
• Photon trapping in static axially symmetric spacetime
• Uniqueness of static photon surfaces: Perturbative approach
• Photon regions and umbilic conditions in stationary axisymmetric spacetimes
• Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory
• Spacetimes containing slowly evolving horizons
• Observability of spherical photon orbits in near-extremal Kerr black holes
• Deformation of Codimension-2 Surface and Horizon Thermodynamics
• Trajectory around a spherically symmetric non-rotating black hole
• Observational distinction between black holes and naked singularities: the role of the redshift function

Cited by in corpus (9)

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• Gravitational lensing by a photon sphere in a Reissner-Nordström naked singularity spacetime in strong deflection limits
• Slice-reducible conformal Killing tensors, photon surfaces and shadows
• Retrolensing by light rays slightly inside and outside of a photon sphere around a Reissner-Nordström naked singularity
• Black hole shadow and Wandering null geodesics
• Quasi-local studies of the particle surfaces and their stability in general spacetimes
• Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory
• Asymptotic behavior of null geodesics near future null infinity II: curvatures, photon surface and dynamically transversely trapping surface