Breakdown of Universal Relations in Charged AdS Black Holes with Non-Extensive Entropy Corrections

Основные понятия

While traditional black hole thermodynamics, using Bekenstein-Hawking entropy, supports universal relations concerning entropy and extremality bounds, introducing non-extensive entropy generalizations disrupts these relations in charged Anti-de Sitter black holes.

Аннотация

• Bibliographic Information: Anand, A., & Gashti, S. N. (2024). Universal Relations with the Non-Extensive Entropy Perspective. arXiv preprint arXiv:2411.02875v1.
• Research Objective: This study investigates the validity of universal relations in black hole thermodynamics when considering non-extensive entropy generalizations, focusing on charged Anti-de Sitter (AdS) black holes.
• Methodology: The authors introduce a minor constant correction (ε) to the black hole metric, perturbing the thermodynamic variables. They then analyze the universal relations using various non-extensive entropy proposals, including Barrow, Kaniadakis, Renyi, Sharma-Mittal, and Tsallis-Cirto entropies.
• Key Findings: The study reveals that the introduction of non-extensive entropy generalizations leads to a breakdown of the universal relations in charged AdS black holes. This finding contrasts with the results obtained using the traditional Bekenstein-Hawking entropy, where the universal relations hold.
• Main Conclusions: The authors conclude that the modifications introduced by non-extensive entropy measures disrupt the expected universal behavior of charged AdS black holes. This suggests a potential incompatibility between the assumptions of universal relations and the framework of non-extensive entropy.
• Significance: This research highlights the limitations of applying non-extensive entropy generalizations to black hole thermodynamics, particularly in the context of universal relations. It suggests the need for further investigation into the underlying principles and potential modifications required to reconcile these differences.
• Limitations and Future Research: The study focuses specifically on charged AdS black holes. Future research could explore the impact of non-extensive entropy on the thermodynamic stability of other black hole types, such as rotating or higher-dimensional black holes. Additionally, investigating the connection between the introduced constant correction (ε) and other physical parameters in black hole physics could provide valuable insights.

Статистика

Цитаты

Ключевые выводы из

Universal Relations with the Non-Extensive Entropy Perspective

by Ankit Anand,... в arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.02875.pdf

Дополнительные вопросы

How might the incorporation of quantum gravity effects beyond the modification of entropy further impact the validity of universal relations in black hole thermodynamics?

Incorporating the full tapestry of quantum gravity effects beyond entropy modification could significantly alter our understanding of black hole thermodynamics and, consequently, the validity of universal relations. Here's how:

Fluctuating Horizons and Non-Locality: Quantum gravity suggests that black hole horizons might not be smooth, classical boundaries but rather fluctuating entities governed by quantum uncertainty. This could introduce non-locality, where the entropy is not strictly localized on the horizon, further complicating the relationship between entropy and other thermodynamic variables.

Discrete Spectra and Quantum Corrections: Quantum gravity might imply a discrete spectrum for black hole observables like mass and charge. These quantizations could introduce corrections to thermodynamic relations, potentially modifying or even invalidating universal relations derived from classical or semi-classical considerations.

Beyond Semi-Classical Gravity: Universal relations are often derived using semi-classical approaches, treating gravity classically while incorporating some quantum effects. However, a full theory of quantum gravity might necessitate a paradigm shift beyond these approximations. New principles and frameworks might emerge, potentially leading to entirely different sets of relations governing black hole thermodynamics.

Information Loss Paradox and Entropy: The information loss paradox, a fundamental puzzle in black hole physics, highlights the tension between quantum mechanics and general relativity regarding information conservation during black hole evaporation. Resolving this paradox within a complete quantum gravity framework could have profound implications for the nature of black hole entropy and its relation to other thermodynamic quantities.
In essence, delving deeper into the quantum gravity realm could reveal that the current understanding of universal relations is a limited view from a semi-classical perspective. A complete picture might necessitate a radical revision of our thermodynamic concepts and their interrelations in the context of black holes.

Could there be specific types of non-extensive entropy generalizations or modifications to the universal relations themselves that would lead to a reconciliation of these concepts in the context of black hole thermodynamics?

It's certainly plausible that specific non-extensive entropy generalizations or modifications to universal relations could bridge the gap between these concepts. Here are some potential avenues for reconciliation:

Modified Dispersion Relations: Some approaches to quantum gravity suggest modifications to the energy-momentum dispersion relation at high energies. These modifications could induce specific forms of non-extensive entropy that naturally satisfy modified universal relations.

Generalized Uncertainty Principles: Generalized uncertainty principles, often motivated by quantum gravity, introduce a minimal length scale and modify the Heisenberg uncertainty principle. These modifications could lead to specific non-extensive entropy expressions compatible with adjusted universal relations incorporating the minimal length scale.

Entanglement Entropy and Holography: The holographic principle suggests a deep connection between gravity and quantum entanglement. Exploring entanglement entropy in the context of black holes and non-extensive statistics might reveal modified universal relations that incorporate entanglement as a key ingredient.

Effective Field Theory Approach: An effective field theory approach to quantum gravity could provide a framework for systematically incorporating quantum corrections to black hole thermodynamics. This could lead to specific non-extensive entropy corrections and corresponding modifications to universal relations, ensuring consistency within the effective field theory framework.

Deformed Spacetime Structures: Some quantum gravity models propose deformed spacetime structures at the Planck scale. These deformations could lead to specific forms of non-extensive entropy that are naturally compatible with modified universal relations reflecting the underlying deformed geometry.
The key lies in finding a consistent framework where the non-extensive nature of entropy emerges naturally from the underlying quantum gravity theory and, in turn, leads to modified universal relations that hold within that framework.

If the universe itself can be considered a thermodynamic system, what implications might the breakdown of universal relations in black holes with non-extensive entropy have for our understanding of cosmological evolution and entropy on a cosmic scale?

The breakdown of universal relations in black holes with non-extensive entropy could have profound implications for our understanding of cosmological evolution and entropy on a cosmic scale, especially if we consider the universe as a thermodynamic system:

Rethinking Cosmic Entropy: The current cosmological model assumes that entropy increases over time, leading to the arrow of time. However, if non-extensive entropy plays a significant role on cosmological scales, our understanding of entropy increase and its connection to cosmic time might need revision.

Dark Energy and Modified Gravity: The accelerated expansion of the universe is attributed to dark energy. If non-extensive entropy modifies black hole thermodynamics, it might also influence the dynamics of the universe, potentially offering new perspectives on dark energy or suggesting modifications to general relativity on cosmological scales.

Early Universe and Inflation: The very early universe, particularly during the inflationary epoch, involved extremely high energies and densities where quantum gravity effects might have been significant. The breakdown of universal relations in this context could imply a different thermodynamic history for the early universe, potentially influencing the formation of structures and the cosmic microwave background radiation.

Holographic Principle and Cosmology: The holographic principle, if applied to the entire universe, suggests that its information content is encoded on its boundary. If non-extensive entropy modifies black hole thermodynamics, it might also impact the holographic description of the universe, potentially leading to new insights into the relationship between quantum information and cosmology.

Arrow of Time and Cosmic Evolution: The arrow of time is often linked to the second law of thermodynamics and the increase of entropy. However, if non-extensive entropy governs the universe's thermodynamics, the arrow of time might not be as straightforward as currently understood. It could be influenced by the specific form of non-extensive entropy and its evolution, potentially leading to alternative scenarios for cosmic evolution.
In essence, the breakdown of universal relations in black holes with non-extensive entropy challenges our fundamental assumptions about entropy and thermodynamics on cosmic scales. It suggests that a deeper understanding of quantum gravity and its interplay with thermodynamics is crucial for unraveling the mysteries of cosmological evolution and the universe's ultimate fate.