Semiclassical Rotating AdS Black Holes with Quantum Hair in Holography

Abstract: In the context of the AdS/CFT duality, we study semiclassical stationary rotating AdS black holes with non-trivial quantum hair in three and five dimensions. We construct these solutions by perturbing the BTZ black hole and the five-dimensional Myers-Perry AdS black hole according to holographic semiclassical equations. In the three-dimensional case, the vacuum expectation value of the stress-energy tensor diverges as $\sim 1/\lambda^n~(n=1,2)$ along a radial null geodesic as the affine parameter $\lambda$ approaches zero at the Cauchy horizon, depending on the type of perturbation. In the five-dimensional case, most hairy solutions exhibit strong divergences, either in the stress-energy tensor or in the parallelly propagated Riemann components, along the radial null geodesic crossing the Cauchy horizon. Nevertheless, there exists a specific class of semiclassical solutions that retain a $C^0$-regular Cauchy horizon, where perturbations remain bounded. For extremal black holes, the vacuum expectation value of the stress-energy tensor diverges along a radial null geodesic transverse to the event horizon in both three and five dimensions, even though all components of the perturbed metric vanish in this limit.

Overview of Semiclassical Rotating AdS Black Holes with Quantum Hair in Holography

The paper "Semiclassical Rotating AdS Black Holes with Quantum Hair in Holography" by Hamaki and Maeda focuses on investigating semiclassical rotating Anti-de Sitter (AdS) black holes within the framework of the AdS/CFT correspondence. The primary objective is to understand the influence of quantum hair on these black holes, particularly near the Cauchy horizon, by adopting a holographic approach.

Key Insights and Methodological Framework

The study leverages the AdS/CFT duality, where gravitational phenomena in a (d+1)-dimensional AdS space are related to a conformal field theory on its (d)-dimensional boundary. The researchers consider the semiclassical evolution of rotating AdS black holes in three and five dimensions, focusing on the Cauchy horizon's stability—a fundamental issue raised by the strong cosmic censorship (SCC) conjecture.

The authors perturb the Banados-Teitelboim-Zanelli (BTZ) black hole in three dimensions and the Myers-Perry AdS black hole in five dimensions, analyzing the resulting semiclassical configurations using holographic techniques. These perturbations are governed by holographic semiclassical equations derived from the Einstein-Hilbert action, extended with boundary conditions that describe the dynamics on the boundary of the AdS space.

Main Findings and Results

1. Three-Dimensional Rotating AdS Black Holes:

   • The vacuum expectation value of the stress-energy tensor displays divergences along radial null geodesics approaching the Cauchy horizon, characterized by terms like (\sim 1/\lambda^n) where (\lambda) is the affine parameter.
   • A class of semiclassical solutions with quantum hair maintains a (C^0)-regular Cauchy horizon, leading to perturbations that remain bounded.
   • In extremal cases, even though the stress-energy tensor diverges, black holes exhibit zero-temperature extremal states with distinctive quantum modifications.

2. Five-Dimensional Rotating AdS Black Holes:

   • The study identifies a complex landscape where most solutions exhibit strong divergences due to quantum effects, both in the stress-energy tensor and the Riemann components.
   • Nonetheless, specific configurations allow the construction of solutions with a (C^0)-regular Cauchy horizon, suggesting a potential avenue to reconcile observations with the SCC conjecture.

Theoretical and Practical Implications

The findings have significant implications for understanding quantum effects on black hole interiors, especially regarding the SCC conjecture. The divergence of the stress-energy tensor near the Cauchy horizon in these higher-dimensional spaces suggests complex interactions between classical and quantum phenomena. These insights can inspire further exploration into the nature of quantum gravity and the role of quantum effects in horizon dynamics.

Speculations on Future Developments

This research opens several avenues for future exploration. Further work could delve into higher-dimensional cases or different configurations within the AdS/CFT framework, potentially offering new quantum gravity insights. The interplay between extremal and non-extremal states and their quantum characteristics provides a fertile ground for theoretical breakthroughs regarding black hole thermodynamics and information paradoxes. Additionally, expanding these methods to include non-rotating solutions or charged black holes could further illuminate how quantum gravity affects black hole interiors across various scenarios.

In conclusion, this paper presents a comprehensive study of semiclassical rotating AdS black holes under quantum perturbations, contributing valuable knowledge to the fields of gravitational physics and holography.