The Instability and Stability Conditions of Planar Black Holes in Gauged N=8 Supergravity

Core Concepts

This paper investigates the thermodynamic stability of planar black holes in the STU model of gauged N=8 supergravity, demonstrating that while purely electric black holes are inherently unstable below a critical temperature, magnetic black holes exhibit stability under specific conditions, particularly when satisfying the topological twist condition and employing a shifted energy definition that vanishes for BPS solutions.

Abstract

Bibliographic Information:

Anabalón, A., Maurelli, S., Oyarzo, M., & Trigiante, M. (2024). The Instability of Low-Temperature Black Holes in Gauged N = 8 Supergravity. arXiv:2411.09454v1 [hep-th].

Research Objective:

This study examines the thermodynamic stability of planar black hole solutions within the framework of the STU model in gauged N=8 supergravity. The authors aim to determine the stability conditions for both electrically and magnetically charged black holes, focusing on the behavior of these solutions at low temperatures.

Methodology:

The authors employ analytical techniques from general relativity and supergravity to derive the equation of state for both electric and magnetic planar black holes. They analyze the Hessian matrix of the energy density to assess the stability of these solutions. For electric black holes, they calculate the determinant of the Hessian to identify instability regions. For magnetic black holes, they incorporate the topological twist condition and introduce a shifted energy definition to investigate stability, particularly in the context of BPS solutions.

Key Findings:

• The study reveals that all extremal electrically charged planar black holes in this model are thermodynamically unstable.
• Even above extremality, there exists a finite temperature range where electric black holes remain unstable.
• In contrast, magnetic planar black holes, particularly those satisfying the topological twist condition, exhibit stability when a shifted energy definition is employed.
• The authors provide a detailed analysis of the stability conditions for both BPS and non-BPS extremal magnetic black hole solutions.

Main Conclusions:

The research demonstrates a fundamental difference in the thermodynamic stability of electric and magnetic planar black holes in the STU model of gauged N=8 supergravity. While electric black holes exhibit inherent instability below a critical temperature, magnetic black holes can achieve stability under specific conditions related to the topological twist and a shifted energy definition.

Significance:

This study contributes significantly to the understanding of black hole thermodynamics in the context of extended supergravity theories. The findings have implications for the study of black hole stability, the AdS/CFT correspondence, and the development of a consistent quantum theory of gravity.

Limitations and Future Research:

The analysis primarily focuses on planar black hole solutions within a specific supergravity model. Further research could explore the stability of black holes with different horizon topologies and in more general supergravity theories. Investigating the implications of these findings for the AdS/CFT correspondence and the microscopic interpretation of black hole entropy would also be of significant interest.

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Key Insights Distilled From

The Instability of Low-Temperature Black Holes in Gauged $\mathcal{N}=8$ Supergravity

by Andr... at arxiv.org 11-15-2024

https://arxiv.org/pdf/2411.09454.pdf

Deeper Inquiries

How do the stability conditions for planar black holes in gauged N=8 supergravity extend to black holes with different horizon topologies, such as spherical or hyperbolic black holes?

Answer:
While the provided context focuses on planar black holes in gauged N=8 supergravity, extending the stability analysis to different horizon topologies (spherical or hyperbolic) introduces significant complexities. Here's a breakdown:

Spherical Black Holes: Spherical black holes in AdS spacetime are generally less stable than their planar counterparts. This is because the negative cosmological constant of AdS acts like a confining box, and the spherical topology can lead to a self-gravitational attraction that favors collapse.

For electrically charged spherical black holes, we can expect an even more pronounced instability compared to the planar case. The attractive nature of gravity combines with the electrostatic repulsion, potentially leading to fragmentation or other non-trivial behavior.
For magnetically charged spherical black holes, the situation is more nuanced. The existence of globally defined Killing spinors and a well-defined BPS limit suggests potential stability for the supersymmetric branch. However, a rigorous analysis involving the Hessian of the energy density, taking into account the topological twist condition and a suitable energy redefinition, is necessary to confirm this.

Hyperbolic Black Holes: Hyperbolic black holes have a negative curvature horizon and are generally considered more stable due to the repulsive nature of gravity in this context.

The context mentions that BPS electric black holes with hyperbolic horizons lead to imaginary gauge fields, making them less physically relevant.
The stability of magnetically charged hyperbolic black holes would require a separate investigation. The presence of a negative curvature horizon might influence the stability conditions compared to the planar case.
Key Considerations for Generalization:

Boundary Conditions: Different horizon topologies imply different boundary conditions at infinity, which can significantly impact the stability analysis.
Hawking Temperature: The Hawking temperature, a crucial factor in thermodynamic stability, will have a different dependence on the black hole parameters for different topologies.
Supersymmetry: The role of supersymmetry in stabilizing black holes can vary with horizon topology. The existence and nature of BPS limits need to be carefully examined.

Could the instability of electric black holes be a consequence of working within a specific supergravity model, and might they become stable in more general or modified theories of gravity?

Answer:
The instability of electric black holes observed in the context of the gauged N=8 supergravity STU model might indeed be a consequence of the specific model and could potentially be altered in more general or modified theories of gravity. Here's why:

Scalar Fields and Couplings: The STU model involves scalar fields (dilatons and axions) with specific couplings to the gauge fields and gravity. These couplings can influence the black hole's stability. Modifying these couplings or considering different scalar field content could change the stability conditions.

Higher-Order Corrections: Supergravity theories are often considered low-energy effective descriptions of more fundamental theories like string theory. Higher-order corrections in these fundamental theories could modify the black hole solutions and potentially stabilize the electric black holes.

Modified Gravity: Moving beyond the realm of supergravity, modified theories of gravity (e.g., adding higher curvature terms to the Einstein-Hilbert action) can drastically alter the black hole solutions and their stability properties.
Examples of Potential Stabilization Mechanisms:

Higher-Derivative Terms: Including higher-derivative terms in the action can introduce new scales and modify the black hole's near-horizon geometry, potentially leading to stability.
Non-Minimal Couplings: Introducing non-minimal couplings between the scalar fields and the curvature could change the effective potential for the scalar fields and stabilize the black hole.
Quantum Corrections: Quantum effects, particularly in the strong gravity regime near the black hole horizon, could provide stabilizing contributions.
Important Note: Determining whether electric black holes become stable in more general settings requires explicit calculations within those specific theories.

What are the implications of these findings for the AdS/CFT correspondence, particularly regarding the duality between black holes in the bulk and thermal states in the boundary conformal field theory?

Answer:
The findings regarding the stability of black holes in gauged N=8 supergravity have intriguing implications for the AdS/CFT correspondence, particularly concerning the duality between black holes in the bulk and thermal states in the boundary conformal field theory (CFT):

Instability and Phase Transitions: The instability of electric black holes suggests a corresponding instability in the dual CFT thermal states. This instability could manifest as a phase transition in the boundary theory at a critical temperature related to the black hole's Hawking temperature. The nature of this phase transition would depend on the specific details of the instability.

Stable Magnetic Black Holes and the CFT: The stability of magnetic black holes, particularly those satisfying the topological twist condition, implies the existence of corresponding stable thermal states in the dual CFT. These states would likely possess special properties related to the supersymmetry of the bulk black hole solutions.

Exploring the CFT Phase Diagram: The stability analysis of black holes with different charges and horizon topologies provides valuable information about the phase diagram of the dual CFT. Regions of stable black holes would correspond to stable phases in the CFT, while unstable black holes suggest phase transitions or critical behavior.

Quantum Information and Black Hole Thermodynamics: The AdS/CFT correspondence provides a powerful framework for understanding black hole thermodynamics from a quantum information perspective. The stability analysis of black holes in the bulk can shed light on the thermal properties and entanglement entropy of the dual CFT states.
Further Research Directions:

Identifying the CFT Duals: A crucial step is to identify the specific CFT operators and states that correspond to the stable and unstable black hole solutions found in the bulk.
Characterizing Phase Transitions: If the black hole instabilities lead to phase transitions in the CFT, characterizing the nature of these transitions (e.g., first-order vs. second-order) would be highly valuable.
Exploring Quantum Corrections: Investigating how quantum corrections in the bulk gravity theory affect the stability of black holes and their implications for the dual CFT is an active area of research.