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The uniqueness of static asymptotically flat photon sphere for static black hole solution in Einstein-Maxwell-dilaton theory with arbitrary coupling constant was proposed. Using the conformal positive energy theorem we show that the dilaton…

High Energy Physics - Theory · Physics 2016-03-09 Marek Rogatko

Properties of the Reissner-Nordstr\"om black-hole and naked-singularity spacetimes with a nonzero cosmological constant are represented by their geodetical structure and embedding diagrams of the central planes of both the ordinary geometry…

General Relativity and Quantum Cosmology · Physics 2008-03-19 Zdeněk Stuchlík , Stanislav Hledík

Photon surfaces are timelike, totally umbilic hypersurfaces of Lorentzian spacetimes. In the first part of this paper, we locally characterize all possible photon surfaces in a class of static, spherically symmetric spacetimes that includes…

Differential Geometry · Mathematics 2021-04-01 Carla Cederbaum , Gregory J. Galloway

We study closed photon orbits in spherically-symmetric static solutions of supergravity theories, a Horndeski theory, and a theory of quintessence. These orbits lie in what we shall call a photon sphere (anti-photon sphere) if the orbit is…

General Relativity and Quantum Cosmology · Physics 2019-04-26 M. Cvetic , G. W. Gibbons , C. N. Pope

The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon surface in an arbitrary space-time. A photon sphere is then defined as an SO(3)xR-invariant photon surface in a static spherically symmetric…

General Relativity and Quantum Cosmology · Physics 2010-02-22 Clarissa-Marie Claudel , K. S. Virbhadra , G. F. R. Ellis

The photon sphere, a hypersurface of circular null geodesics, plays a fundamental role in characterizing black hole spacetimes, influencing phenomena such as black hole shadows, gravitational lensing, and quasinormal modes. While universal…

General Relativity and Quantum Cosmology · Physics 2026-02-25 Yong Song , Jiaqi Fu , Yiting Cen

We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the…

General Relativity and Quantum Cosmology · Physics 2009-10-30 Jarmo Makela , Pasi Repo

The photon surface is defined as a timelike surface $S$ such that any photon emitted in arbitrary tangential direction to $S$ from an arbitrary point on $S$ continues to propagate on $S$. In this paper, we examine whether a static photon…

General Relativity and Quantum Cosmology · Physics 2023-09-26 Hirotaka Yoshino

To understand the nature of a black hole shadow in dynamical spacetimes, we construct an analytical model of a dynamical photon sphere in the context of the Bonnor-Vaidya spacetime. Comparing the resulting photon sphere radius with the one…

General Relativity and Quantum Cosmology · Physics 2024-09-11 Yaghoub Heydarzade , Vitalii Vertogradov

A photon surface $S$ is defined as a three-dimensional timelike hypersurface such that any null geodesic initially tangent to $S$ continues to be included in $S$, like $r=3M$ of the Schwarzschild spacetime. Using analytic solutions to…

General Relativity and Quantum Cosmology · Physics 2017-03-08 Hirotaka Yoshino

This paper investigates the photon ring and shadow structure of the Reissner-Nordstr\"om black hole in the scalar-tensor-vector gravitational framework. The black hole is characterized by the ( MOG) parameter (\alpha) and the charge (Q).…

General Relativity and Quantum Cosmology · Physics 2026-02-04 Qiao Yue , Zhaoyi Xu , Meirong Tang

In this work, we establish the existence conditions and a universal upper bound on the radius of stable photon spheres (SPS) outside the event horizons of static, spherically symmetric, asymptotically flat black holes surrounded by matter…

General Relativity and Quantum Cosmology · Physics 2025-09-16 Yong Song , Jiaqi Fu , Yiting Cen

We investigate strong gravitational lensing by a marginally unstable photon sphere in a Reissner-Nordstr\"{o}m naked singularity spacetime. Using the Picard-Fuchs equation, we derive full-order power series expressions for the deflection…

General Relativity and Quantum Cosmology · Physics 2025-12-10 Tadashi Sasaki

It has been shown in the literature that the event horizon of an extremal asymptotically flat Reissner-Nordstrom black hole is also a stable photon sphere. We further clarify this statement and give a general proof that this holds for a…

General Relativity and Quantum Cosmology · Physics 2017-07-31 Fech Scen Khoo , Yen Chin Ong

In this paper we examine the relativistic Einstein rings assuming a nonminimal coupling between gravitation and electromagnetism in a Reissner-Norstr\"om background. Starting from a general action of a nonminimal coupled electrodynamics we…

General Relativity and Quantum Cosmology · Physics 2025-01-31 Rodrigo Maier

We consider the optical appearance of a non-singular, spherically symmetric black hole from Eddington-inspired Born-Infeld gravity coupled to anisotropic fluids. Such a black hole has a single (external) horizon located very near the…

General Relativity and Quantum Cosmology · Physics 2026-05-01 David Díaz-Guerra , Angel Rincon , Diego Rubiera-Garcia

We consider the bending angle of the trajectory of a photon incident from and deflected to infinity around a Reissner-Nordstr\"om black hole. We treat the bending angle as a function of the squared reciprocal of the impact parameter and the…

General Relativity and Quantum Cosmology · Physics 2023-12-04 Tadashi Sasaki

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…

General Relativity and Quantum Cosmology · Physics 2021-09-23 Li-Ming Cao , Yong Song

In this article we extend a recent theorem proven by Hod (Phys. Lett. B, {\bf 727}, 345--348, 2013) to $n$-dimensional Einstein and Einstein-Gauss-Bonnet theories, which gives an upper bound for the photon sphere radii of spherically…

General Relativity and Quantum Cosmology · Physics 2016-09-01 Emanuel Gallo , J. R. Villanueva

We study isoperimetric surfaces in the Reissner-Nordstr\"om spacetime, with emphasis on the cuasilocal inequality between area and charge. We analyze the stability of the isoperimetric spheres and we found that there is a lower bound on the…

General Relativity and Quantum Cosmology · Physics 2015-06-11 Andrés E. Aceña , Sergio Dain