Observing black hole phase transitions in extended phase space and holographic thermodynamics approaches from optical features

Chatchai Promsiri; Weerawit Horinouchi; Ekapong Hirunsirisawat

doi:10.1140/epjc/s10052-025-14221-x

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 484
https://doi.org/10.1140/epjc/s10052-025-14221-x

Regular Article - Theoretical Physics

Observing black hole phase transitions in extended phase space and holographic thermodynamics approaches from optical features

Chatchai Promsiri¹, Weerawit Horinouchi² and Ekapong Hirunsirisawat¹^,3^a

¹ Quantum Computing and Information Research Centre (QX), Faculty of Science, King Mongkut’s University of Technology Thonburi, 10140, Bangkok, Thailand
² High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, 10330, Bangkok, Thailand
³ Learning Institute, King Mongkut’s University of Technology Thonburi, 10140, Bangkok, Thailand

^a ekapong.hir@kmutt.ac.th

Received: 10 March 2025
Accepted: 22 April 2025
Published online: 4 May 2025

Abstract

The phase transitions of charged Anti-de Sitter (AdS) black holes are characterized by studying null geodesics in the vicinity of the critical curve of photon trajectories around black holes as well as their optical appearance as the black hole images. In the present work, the critical parameters including the orbital half-period $τ,$ $\tau ,$ the angular Lyapunov exponent $λ_{L},$ $\lambda _L,$ and the temporal Lyapunov exponent $γ_{L}$ $\gamma _L$ are employed to characterize black hole phase transitions within both the extended phase space and holographic thermodynamics frameworks. Under certain conditions, we observe multi-valued function behaviors of these parameters as functions of bulk pressure and temperature in the respective approaches. We propose that $τ,$ $\tau ,$ $λ_{L},$ $\lambda _L,$ and $γ_{L}$ $\gamma _L$ can serve as order parameters due to their discontinuous changes at first-order phase transitions. To validate this, we provide detailed analytical calculations demonstrating that these optical critical parameters follow scaling behavior near the critical phase transition point. Notably, the critical exponents for these parameters are found to be 1/2, consistent with those of the van der Waals fluid. Our findings suggest that static and distant observers can study black hole thermodynamics by analyzing the images of regions around the black holes.

© The Author(s) 2025

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