Effective Potential and Topological Photon Spheres: A Novel Approach to Black Hole Parameter Classification

Abstract

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, we categorize the behaviors of various gravitational models based on the structure of their photon spheres. This innovative approach enables us to define boundaries for black hole parameters, subsequently allowing us to classify the model as either a black hole or a naked singularity. Indeed, we will demonstrate that the presence of this interplay between the gravitational structure and the existence of a photon sphere is a unique advantage that can be utilized from both perspectives. Our observations indicate that a gravitational model typically exhibits the behavior of a horizonless structure (or a naked singularity) when a minimum effective potential (a stable photon sphere) appears within the studied spacetime region. Additionally, in this study, we tried to investigate the effect of this structure on the behavior of the photon sphere by choosing models that are affected by the Perfect Fluid Dark Matter (PFDM). Finally, by analyzing a model with multiple event horizons, we show that the proposed method remains applicable even in such scenarios.

41 pages, 16 figures, 7 Tables, Accepted manuscript for publication in Chinese Physics C

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• Weak Gravity Conjecture Validation with Photon Spheres of Quantum Corrected AdS-Reissner-Nordstrom Black Holes in Kiselev Spacetime
• Non-extensive Entropy and Holographic Thermodynamics: Topological Insights
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• Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordström AdS Black Holes
• Assessing WGC Compatibility in ModMax Black Holes via Photon Spheres Analysis and WCCC Validation
• Thermodynamic Topology and Photon Spheres Analysis of Black Holes in Brane-World: Insights from Barrow Entropy
• Overcoming Barriers: Kramers' Escape Rate Analysis of Metastable Dynamics in First-Order Multi-Phase Transitions
• Topological charge and black hole photon spheres in massive gravity