[Paper Review] Thermal fluctuations of charged black hole solution in Rastall theory

Behnam Pourhassan, Sudhaker Upadhyay|arXiv (Cornell University)|Oct 23, 2019

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates thermal fluctuations in charged black holes within Rastall gravity, considering quintessence, dust, and radiation fields. It shows that thermal fluctuations increase instability, induce second-order phase transitions, and disrupt Van der Waals behavior in small black holes, while large black holes retain such behavior; corrected thermodynamics and scalar curvature are also analyzed via geometric thermodynamics.

ABSTRACT

We study the thermodynamics of a charged black hole surrounded by a perfect fluid in Rastall theory and investigate three different cases of quintessence, dust and radiation fields. By considering thermal fluctuations, we study corrected thermodynamics variables. We investigate the effects of thermal fluctuations on the black hole stability, phase transition and critical points. We show that thermal fluctuations make the black hole more unstable and may yields to the second order phase transition. We also compare our results with uncharged cases to find effects of the black hole charge on the thermodynamics quantities. We find that large black holes behave like a Van der Waals fluid, while for the small black hole where thermal fluctuations become important, there is no Van der Waals behavior. Finally we discuss in brief about geometric thermodynamics to obtain corrected scalar curvature.

Motivation & Objective

• To analyze the thermodynamic behavior of charged black holes in Rastall gravity coupled with perfect fluid fields (quintessence, dust, radiation).
• To investigate the impact of thermal fluctuations on black hole stability, phase transitions, and critical points.
• To compare thermodynamic properties of charged versus uncharged black holes in the context of thermal corrections.
• To examine whether small black holes with significant thermal fluctuations still exhibit Van der Waals-like behavior.
• To apply geometric thermodynamics to derive corrected scalar curvature for the black hole system.

Proposed method

• Formulate the metric and thermodynamic quantities (entropy, temperature, heat capacity) for a charged black hole in Rastall theory with a perfect fluid source.
• Apply the thermal fluctuation correction framework to derive modified expressions for entropy, internal energy, and heat capacity.
• Analyze the corrected heat capacity to determine thermodynamic stability and identify phase transitions.
• Use the corrected thermodynamic potentials to locate critical points and assess the presence of Van der Waals-like behavior.
• Employ geometric thermodynamics to compute the corrected scalar curvature, linking curvature singularities to phase transitions.
• Compare results across three fluid types (quintessence, dust, radiation) and for both charged and uncharged cases.

Experimental results

Research questions

• RQ1 How do thermal fluctuations affect the thermodynamic stability of charged black holes in Rastall gravity with different fluid fields?
• RQ2 What is the role of black hole charge in modifying phase transition behavior under thermal fluctuations?
• RQ3 Do small black holes with strong thermal fluctuations still exhibit Van der Waals-like thermodynamic behavior?
• RQ4 Can second-order phase transitions be induced by thermal fluctuations in this system?
• RQ5 How does the corrected scalar curvature in geometric thermodynamics reflect critical phenomena in the black hole system?

Key findings

• Thermal fluctuations significantly increase the instability of charged black holes, particularly in small systems where quantum effects dominate.
• Thermal fluctuations can induce a second-order phase transition, indicated by divergences in the corrected heat capacity.
• Large black holes retain Van der Waals-like behavior, but this behavior breaks down in small black holes due to dominant thermal corrections.
• The presence of charge alters thermodynamic quantities compared to the uncharged case, especially in the magnitude and sign of heat capacity corrections.
• The corrected scalar curvature in geometric thermodynamics exhibits singularities at critical points, confirming the presence of phase transitions.
• The thermodynamic behavior differs markedly between quintessence, dust, and radiation fields, with quintessence showing the most pronounced effects on criticality.