Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

Abstract: We obtain an exact solution of spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter (PFDM). Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable, we analyse the thermodynamics of our black holes in the extended phase space. Owing to the background clouds of strings parameter ($a$) and the parameter endowed with PFDM ($\beta$), we analyse the Hawking temperature, entropy and specific heat. We also investigate the relationship between the photon sphere radius and the phase transition for the Letelier AdS black holes immersed in PFDM. Through the analysis, we find with a particular condition, there are non-monotonic behaviours between the photon sphere radius, the impact parameter, the PFDM parameter, temperature, and pressure. We can regard both the changes of photon sphere radius and impact parameter before and after phase transition as the order parameter; their critical exponents near the critical point are equal to the same value 1/2, just like ordinary thermal systems. These indicate that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

• The paper demonstrates that photon orbits act as order parameters for second-order phase transitions in Letelier AdS black holes with perfect fluid dark matter.
• Authors derive a spherically symmetric solution by treating the cosmological constant as pressure and incorporating clouds of string parameters to analyze thermodynamics.
• Numerical analyses reveal critical behavior, matching van der Waals-like phase transitions with quantified critical exponents of 1/2 for the black hole system.

Phase Transitions and Photon Orbits in Letelier AdS Black Holes

The paper "Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter" investigates the intriguing relationship between photon sphere radii, phase transitions, and thermodynamics of Letelier black holes influenced by perfect fluid dark matter.

Introduction

Letelier AdS black holes, extended to include perfect fluid dark matter (PFDM), form the basis of this research. These systems are analyzed by considering the cosmological constant as a pressure, exploring their thermodynamic properties. Theoretical predictions and numerical calculations reveal how photon orbits, critical properties, and phase transitions interrelate, leading to conclusions about the thermodynamics of such black holes infused with PFDM.

Black Hole Solution and Thermodynamic Properties

The authors derive a spherically symmetric solution for Letelier AdS black holes immersed in PFDM, accounting for clouds of string parameters and a cosmological constant as pressure. The fundamental thermodynamic properties—mass, temperature, entropy, and pressure—are explored within an extended phase space framework, leading to the identification of phase transitions akin to those found in van der Waals fluids. The stability of the black hole system is gauged with specific heat and Gibbs free energy, revealing conditions for stable and unstable phases.

Photon Orbits and Critical Behavior

The connection between photon orbits and thermodynamic phase transitions is a novel aspect explored. The photon sphere radius is analytically expressed, providing insights into the nature of unstable photon orbits near critical points of the system. This study equates changes in photon sphere radii and impact parameters before and after phase transitions, proposing these as order parameters. The authors identify critical exponents, equal to 1/2, showing that photon orbits reveal second-order phase transitions.

Results and Implications

The study surfaces several key findings:

• Letelier AdS black holes exhibit thermodynamic behaviors reminiscent of van der Waals fluids, with first and second-order phase transitions evident in their thermodynamic and photon sphere properties.
• The correlation between photon orbits and phase transitions suggests a deeper thermodynamic structure, pointing to universal properties in gravity and thermodynamics.
• Numerical analyses demonstrate critical phenomena occurring in photon sphere radii and impact parameters, offering a new method to study such black hole systems.

Conclusion

In bridging photon orbits with thermodynamics, this research offers a fresh perspective on black hole analysis. It particularly emphasizes that the study of unstable photon orbits can reveal critical phase transition behaviors in black hole systems with PFDM, suggesting possible universality in black hole thermodynamics. This could open pathways to new theoretical frameworks exploring the nature of black holes, including their thermodynamic interactions in a cosmological context.

The implications for both theoretical exploration and potential observational studies (such as black hole shadows) underscore the relevance of aligning gravitational properties with thermodynamic concepts—a promising step toward a comprehensive understanding of black holes in the context of astrophysical environments.