Photon surfaces in spherically, planar and hyperbolically symmetric spacetimes of D-dimensions: Sonic point/photon sphere correspondence

Abstract

Sonic point/photon sphere (SP/PS) correspondence is a theoretical phenomenon which appears in fluid dynamics on curved spacetime and its existence has been recently proved in quite wide situations as theorems. The theorems state that a sonic point (SP) of radiation fluid flow must be on an unstable photon sphere (PS) when the fluid flows radially or rotationally on an equatorial plane in spherically symmetric spacetime of arbitrary dimensions. In this paper, we investigate SP/PS correspondence in spherically, planarly and hyperbolically symmetric spacetime. As the corresponding objects of photon spheres in non-spherically symmetric spacetime, we consider photon surfaces introduced by Claudel {\it et al.} (2001) in the spacetime. After formulating the problem of radial fluid flows, we prove there always exists a correspondence between the sonic points and the photon surfaces, namely, SP/PS correspondence in non-spherically symmetric spacetime.

arXiv comment15 pages

References in corpus (8)

• Geodesic stability, Lyapunov exponents and quasinormal modes
• The geometry of photon surfaces
• Pair Production of Topological anti de Sitter Black Holes
• Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation
• Spherical steady accretion flows -- dependence on the cosmological constant, exact isothermal solutions and applications to cosmology
• Radial accretion flows on static spherically symmetric black holes
• The correspondence between sonic points of ideal photon gas accretion and photon spheres
• Rotating accretion flows in $D$ dimensions: sonic points, critical points and photon spheres

Cited by in corpus (17)

• Gravitational lensing in the Simpson-Visser black-bounce spacetime in a strong deflection limit
• Transversely trapping surfaces: Dynamical version
• Gravitational lensing by a photon sphere in a Reissner-Nordström naked singularity spacetime in strong deflection limits
• Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit
• Nonlogarithmic divergence of a deflection angle by a marginally unstable photon sphere of the Damour-Solodukhin wormhole in a strong deflection limit
• Dynamical photon sphere and time evolving shadow around black holes with temporal accretion
• Stability of null orbits on photon spheres and photon surfaces
• Photon surfaces as pure tension shells: Uniqueness of thin shell wormholes
• Photon surfaces in less symmetric spacetimes
• Spherical Accretion Flow onto General Parameterized Spherically Symmetric Black Hole Spacetimes
• Nondivergent deflection of light around a photon sphere of a compact object
• Circular light orbits of a general, static, and spherical symmetrical wormhole with $Z_2$ symmetry
• Relation between circular photon orbits and the stability of wormholes with the thin shell of a barotropic fluid
• Sonic Point and Photon Surface
• Gravitational lensing by two photon spheres in a black-bounce spacetime in strong deflection limits
• Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits
• Test particle motion around a black hole dressed with a spherically symmetric stationary fluid