Thermodynamics of Einstein-Gauss-Bonnet Black Holes: An Ensemble-Averaged Approach

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Incorporating non-classical geometries into the thermodynamic analysis of black holes in Einstein-Gauss-Bonnet gravity reveals that the sharp phase transitions observed in the classical limit are likely a consequence of the small-GN approximation and that the similarities in thermodynamic behavior between different types of black holes extend beyond the classical regime.

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• Bibliographic Information: Ali, M.S., Fairoos, C., Rizwan, C.L.A., Safir, T.K., & Cheng, P. (2024). Thermodynamics of Einstein-Gauss-Bonnet Black Holes and Ensemble-averaged Theory. arXiv preprint arXiv:2411.07147v1.

• Research Objective: To investigate the thermodynamics of Einstein-Gauss-Bonnet (EGB) black holes in Anti-de Sitter (AdS) spacetime beyond the classical limit by applying the ensemble-averaged theory.

• Methodology: The authors utilize the ensemble-averaged theory to calculate the gravitational partition function by incorporating non-saddle geometries, contrasting with the traditional saddle-point approximation. They numerically evaluate the ensemble-averaged free energy for five and six-dimensional EGB-AdS black holes at various values of Newton's gravitational constant (GN). Additionally, they expand the ensemble-averaged free energy in powers of GN to identify quantum corrections at subleading and sub-subleading orders.

• Key Findings:

  • The ensemble-averaged free energy, which accounts for non-classical geometries, does not exhibit the sharp phase transition points observed in the classical free energy calculations.
  • As GN approaches zero, the ensemble-averaged free energy converges to the classical free energy, suggesting that the sharp phase transitions are a feature of the small-GN limit.
  • The sub-leading term in the GN expansion of the ensemble-averaged free energy is TH/2, consistent with findings for other black hole types, suggesting a universal characteristic.
  • The quantum-corrected free energy for a six-dimensional EGB black hole reveals a local minimum, absent in the classical analysis, aligning with observations for Schwarzschild-AdS black holes.

• Main Conclusions: The study reveals that incorporating non-classical geometries through the ensemble-averaged theory significantly alters the understanding of EGB black hole thermodynamics. The absence of sharp phase transitions in the ensemble-averaged picture suggests a smoother thermodynamic behavior. The similarities observed between different black hole types, even beyond the classical limit, hint at underlying connections and universal features in black hole thermodynamics.

• Significance: This research provides a more comprehensive framework for understanding black hole thermodynamics by moving beyond the limitations of the classical saddle-point approximation. The findings have implications for the development of a complete statistical description of black hole thermodynamics and the ongoing quest to understand quantum gravity.

• Limitations and Future Research: The study focuses on specific dimensions (five and six) for EGB-AdS black holes. Exploring the ensemble-averaged theory in other dimensions and for different gravitational theories would provide a more complete picture. Further investigation into the physical interpretations of the subleading and higher-order corrections in the GN expansion could offer deeper insights into the quantum nature of gravity.

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Thermodynamics of Einstein-Gauss-Bonnet Black Holes and Ensemble-averaged Theory

by Md Sabir Ali... ที่ arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.07147.pdf

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How does the inclusion of quantum corrections affect the interpretation of the holographic duality in the context of EGB-AdS black holes?

The inclusion of quantum corrections, as captured by the ensemble-averaged theory, offers a refined perspective on the holographic duality in the context of EGB-AdS black holes. Here's how:

Smoother Phase Transitions: The sharp phase transitions observed in the classical treatment of EGB-AdS black holes, analogous to those in RN-AdS and Schwarzschild-AdS spacetimes, become smoother when quantum corrections are incorporated. This suggests a more nuanced and potentially realistic picture of the duality. Instead of abrupt changes in the boundary CFT corresponding to sharp transitions, the smoother behavior implies a more gradual change in the CFT's degrees of freedom.

Beyond Classical Geometry: The ensemble-averaged theory goes beyond the saddle-point approximation, which focuses solely on classical black hole solutions. By considering contributions from non-classical geometries, we gain insights into the quantum nature of the gravitational theory. This is crucial for the AdS/CFT correspondence, as it provides a window into the quantum behavior of the dual CFT.

Quantum Corrections to Free Energy: The leading-order quantum correction to the free energy, being proportional to the Hawking temperature, has a universal character across different spacetime dimensions and even different gravitational theories. This universality hints at a fundamental aspect of quantum gravity that could be further illuminated through the duality.

New Features in Free Energy Landscape: The emergence of new features in the free energy landscape, such as the local minimum observed in the six-dimensional EGB-AdS case, suggests richer physics at the quantum level. These features could correspond to novel phases or transitions in the dual CFT, enriching our understanding of strongly coupled quantum field theories.
In essence, incorporating quantum corrections through the ensemble-averaged theory refines the holographic dictionary, providing a more complete and potentially accurate mapping between the gravitational dynamics in the bulk AdS spacetime and the quantum phenomena in the boundary CFT.

Could the smoother thermodynamic behavior observed in the ensemble-averaged theory be an artifact of the specific method used, or does it reflect a genuine feature of quantum gravity?

The smoother thermodynamic behavior observed in the ensemble-averaged theory is likely not an artifact of the method but rather a strong indication of a genuine feature of quantum gravity. Here's why:

Universality across Dimensions and Theories: The smoothing effect is consistently observed across different spacetime dimensions (five and six) and even extends to other gravity theories like Einstein gravity in AdS spacetime. This universality makes it less likely to be a mere artifact of the ensemble-averaged approach.

Beyond Saddle-Point Approximation: The ensemble-averaged theory goes beyond the classical saddle-point approximation by incorporating contributions from non-classical geometries. These contributions are naturally expected to smooth out sharp transitions that are solely a feature of the dominant classical saddle point.

Analogy with Statistical Mechanics: The smoothing effect is reminiscent of similar phenomena in statistical mechanics, where thermal fluctuations smooth out sharp phase transitions that would be predicted by considering only the ground state. This analogy further supports the physical relevance of the observed behavior.

Quantum Nature of Gravity: The smoothing of thermodynamic behavior aligns with the general expectation that quantum effects tend to introduce fuzziness and uncertainty, blurring sharp classical boundaries.
However, further investigation is needed to solidify this interpretation:

Exploring Different Averaging Schemes: Examining the impact of different averaging schemes or choices of the ensemble could help rule out potential biases introduced by the specific method.

Microscopic Understanding: A deeper microscopic understanding of the degrees of freedom contributing to the ensemble average would provide stronger evidence for the genuineness of the observed smoothing.
While more research is necessary, the consistency and universality of the smoother thermodynamic behavior in the ensemble-averaged theory strongly suggest that it reflects a genuine feature of quantum gravity, highlighting the limitations of purely classical descriptions of black hole thermodynamics.

How can the insights gained from studying black hole thermodynamics in higher-curvature gravity theories, such as EGB gravity, inform our understanding of the early universe and its evolution?

Studying black hole thermodynamics in higher-curvature gravity theories like EGB gravity provides valuable insights that can significantly inform our understanding of the early universe and its evolution. Here's how:

Beyond Einstein Gravity: Higher-curvature gravity theories, including EGB gravity, are natural extensions of Einstein's general relativity, introducing terms involving higher powers of the curvature tensor. These theories are motivated by attempts to quantize gravity and often arise as low-energy effective descriptions of string theory.

Early Universe as a Quantum Gravity Regime: The very early universe, characterized by extremely high energy densities and curvatures, is expected to be a regime where quantum gravity effects are significant. Therefore, understanding higher-curvature gravity theories is crucial for probing the physics of the early universe.

Inflation and Cosmological Phase Transitions: Higher-curvature terms can significantly modify the dynamics of the early universe, potentially providing mechanisms for inflation or influencing the nature of cosmological phase transitions. The thermodynamic behavior of black holes in these theories could offer clues about the phase structure of the early universe.

Black Holes as Probes of High-Energy Physics: Black holes are extreme environments where gravity is incredibly strong. Studying their thermodynamics in higher-curvature theories allows us to probe the behavior of gravity at high energies, which is relevant for understanding the early universe.

Holographic Cosmology: The AdS/CFT correspondence, which relates gravitational theories to quantum field theories, can be extended to cosmological settings. Insights from black hole thermodynamics in higher-curvature gravity could be translated, via holography, to understand the evolution of the early universe and the quantum nature of spacetime.

Quantum Corrections and Early Universe Evolution: The ensemble-averaged theory and the inclusion of quantum corrections in black hole thermodynamics highlight the importance of going beyond classical descriptions. These corrections could have significant implications for the early universe's evolution, potentially affecting the formation of structures or the generation of primordial gravitational waves.
By studying black hole thermodynamics in higher-curvature gravity theories like EGB gravity, we gain valuable tools and insights to explore the extreme conditions of the early universe, paving the way for a deeper understanding of its quantum nature and evolution.