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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

We have derived the differential equation governing the evolution of the photon sphere for dynamical black hole spacetimes with or without spherical symmetry. Numerical solution of the same depicting evolution of the photon sphere has been…

General Relativity and Quantum Cosmology · Physics 2019-06-05 Akash K Mishra , Sumanta Chakraborty , Sudipta Sarkar

In this paper we derive exact analytical formulas for the evolution of the photon sphere and for the angular radius of the shadow in a special Vaidya spacetime. The Vaidya metric describes a spherically symmetric object that gains or loses…

General Relativity and Quantum Cosmology · Physics 2022-04-01 Jay Solanki , Volker Perlick

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

Black hole thermodynamics is a crucial and foundational aspect of black hole physics, yet its observational verification remains exceptionally challenging. The photon sphere of a black hole, a manifestation of strong gravitational effects,…

General Relativity and Quantum Cosmology · Physics 2025-12-29 Si-Jiang Yang , Shan-Ping Wu , Shao-Wen Wei , Yu-Xiao Liu

There are circular planar null geodesics at $r=3M$ around a Schwarzschild black hole of mass $M$. These geodesics form a photon sphere. Null geodesics of the Schwarzschild space-time which do not form the photon sphere are either escape to…

General Relativity and Quantum Cosmology · Physics 2017-11-03 Andrey A. Shoom

Photon spheres have attracted considerable interest in the studies of black holes and other astrophysical objects. For different categories of spacetimes (or gravitational sources), the existence of photon spheres and their distributions…

General Relativity and Quantum Cosmology · Physics 2026-02-05 Chen-Kai Qiao , Ping Su , Yang Huang

Photon sphere has attracted significant attention since the capture of black hole shadow images by Event Horizon Telescope. Recently, a number of studies have highlighted that the number of photon spheres and their distributions near black…

General Relativity and Quantum Cosmology · Physics 2025-02-25 Chen-Kai Qiao

In a recent work PRD 106, L021501 (2022), a new geometric approach is proposed to obtain the photon sphere (circular photon orbit) and the black hole shadow radius. In this approach, photon spheres and the black hole shadow radius are…

General Relativity and Quantum Cosmology · Physics 2022-11-11 Chen-Kai Qiao

We develop a compact and transparent framework for photon dynamics and shadow formation in slowly evolving, spherically symmetric spacetimes. Starting from the Eddington-Finkelstein action, we derive a force-decomposed radial equation in…

General Relativity and Quantum Cosmology · Physics 2026-02-10 Vitalii Vertogradov , Ali Övgün

Causal concept for the general black hole shadow is investigated, instead of the photon sphere. We define several `wandering null geodesics' as complete null geodesics accompanied by repetitive conjugate points, which would correspond to…

General Relativity and Quantum Cosmology · Physics 2020-10-15 Masaru Siino

In this paper, we first consider null geodesics of a class of charged, spherical and asymptotically flat hairy black holes in an Einstein-Maxwell-scalar theory with a non-minimal coupling for the scalar and electromagnetic fields.…

General Relativity and Quantum Cosmology · Physics 2021-07-07 Qingyu Gan , Peng Wang , Houwen Wu , Haitang Yang

The photon sphere defines the unstable circular orbit of photons in a black hole spacetime. Photons emitted by a source located inside the photon sphere can be gravitationally lensed by the black hole and have time delays when reaching the…

High Energy Astrophysical Phenomena · Physics 2025-05-28 Yuan-Xing Gao

We investigate the dynamic shadows of a black hole with a self-interacting massive complex scalar hair. The complex scalar field \psi evolves with time t, and its magnitude on the apparent horizon |\psi_{h}| starts from zero, undergoes a…

General Relativity and Quantum Cosmology · Physics 2025-11-25 Mingzhi Wang , Cheng-Yong Zhang , Songbai Chen , Jiliang Jing

We consider a class of static and spherically symmetric black hole geometries endowed with a photon sphere. On the one hand, we show that close to the photon sphere, a massless scalar field theory exhibits a simple dynamical…

General Relativity and Quantum Cosmology · Physics 2022-03-24 Bernard Raffaelli

In this paper, we investigate the topological photon sphere from two distinct perspectives. In the first view, we examine the existence and characteristics of topological photon(anti-photon)spheres for black holes with different structures,…

General Relativity and Quantum Cosmology · Physics 2024-08-15 Jafar Sadeghi , Mohammad Ali S. Afshar

Recent observations of black hole shadows have revolutionized our ability to probe gravity in extreme environments. This manuscript presents a novel analytic method to calculate, in leading-order terms, the key parameters of photon sphere…

General Relativity and Quantum Cosmology · Physics 2024-06-04 Vitalii Vertogradov , Ali Övgün

Photon spheres play a pivotal role in the imaging of luminous objects near black holes. In this paper, we examine observational appearances of a star freely falling in hairy black holes, which can possess one or two photon spheres outside…

General Relativity and Quantum Cosmology · Physics 2022-07-07 Yiqian Chen , Guangzhou Guo , Peng Wang , Houwen Wu , Haitang Yang

Under very general assumptions on the accretion flow geometry, images of a black hole illuminated by electromagnetic radiation display a sequence of photon rings (demagnified and rotated copies of the direct image) which asymptotically…

General Relativity and Quantum Cosmology · Physics 2024-07-24 Maciek Wielgus

In this paper, we base our analysis on the assumption that the existence of a photon sphere is an intrinsic feature of any ultra-compact gravitational structure with spherical symmetry. Utilizing the concept of a topological photon sphere,…

General Relativity and Quantum Cosmology · Physics 2024-12-24 Mohammad Ali S. Afshar , Jafar Sadeghi
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