We consider a charged BTZ black hole in asymptotically AdS space-time of
massive gravity to study the effect of the thermal fluctuations on the black
hole thermodynamics. We consider the Einstein-Born-Infeld solution and
investigate critical points and stability. We also compare the results with the
case of Einstein-Maxwell solutions. Besides, we find that thermal fluctuations,
which appear as a logarithmic term in the entropy, affect the stability of the
black hole and change the phase transition point. Moreover, we study the
geometrical thermodynamics and find that the behaviour of the linear Maxwell
solution is the same as the nonlinear one.
Future Roadmap
The conclusions of the study on the charged BTZ black hole in asymptotically AdS space-time of massive gravity highlight the effect of thermal fluctuations on black hole thermodynamics and stability. The study also compares the results with the case of Einstein-Maxwell solutions and investigates critical points. Additionally, the study examines geometrical thermodynamics and analyzes the behavior of linear and nonlinear Maxwell solutions.
Potential Challenges
- Further research may be necessary to explore the implications of thermal fluctuations on black hole stability in more complex gravity theories.
- The comparison of results with Einstein-Maxwell solutions opens up questions regarding the generality of the findings across different gravitational models.
- Understanding the exact nature of the logarithmic term in the entropy and its long-term effects on black hole thermodynamics may require additional investigations.
- Exploring the impact of thermal fluctuations on phase transition points could present challenges in terms of analytic calculations and numerical simulations.
Potential Opportunities
- Continued exploration of thermal fluctuations in black hole thermodynamics could lead to a deeper understanding of the interplay between gravity and thermodynamic properties.
- Further comparisons with different gravitational solutions could provide insights into the robustness and universality of the observed effects.
- Investigating geometrical thermodynamics in more diverse black hole configurations may reveal new relationships and patterns.
- Exploring the behavior of linear and nonlinear Maxwell solutions opens up possibilities for studying the impact of different electromagnetic interactions on black hole stability.
Note: This roadmap represents potential directions for future research based on the conclusions of the provided text. It is not an exhaustive list of all possible avenues, but serves as a starting point for readers interested in further exploration.
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