Kerr-AdS type higher dimensional black holes with non-spherical cross-sections of horizons (2501.05543v2)

Abstract: We construct, in even spacetime dimensions, a family of singularity-free Kerr-Anti-de Sitter-like black holes with negatively curved cross-sections of conformal infinity and non-spherical cross-sections of horizons.

• The paper introduces higher-dimensional Kerr-AdS black holes with non-spherical horizons, expanding traditional spherical models.
• It employs Kerr-Schild metrics and conformal compactification to demonstrate stability and absence of curvature singularities under specific mass and spin conditions.
• The research highlights implications for gravitational thermodynamics and the AdS/CFT correspondence, paving the way for future theoretical explorations.

An Exploration of Higher-Dimensional Kerr-AdS Black Holes with Non-Spherical Horizons

This essay provides a detailed analytical overview of the academic paper authored by Piotr T. Chruściel, Wan Cong, and Finnian Gray, which explores the existence and properties of a novel class of higher-dimensional Kerr-Anti-de Sitter (Kerr-AdS) black hole solutions. These solutions are characterized by a unique feature: non-spherical cross-sections of their horizons. This research extends the landscape of known black hole solutions by introducing configurations with negatively curved cross-sections at infinity, emphasizing their stationarity outside of the event horizon in even spacetime dimensions.

Overview of Kerr-AdS Black Holes

Kerr-AdS black holes, significant due to their profound implications in both gravitational thermodynamics and the AdS/CFT correspondence, accommodate a non-zero cosmological constant ($\Lambda$). Traditionally, the paper has concentrated on spherical horizon geometries, primarily because of their mathematical tractability and symmetry properties. However, the paper in question diverges from this tradition by investigating the implications of allowing non-spherical horizon geometries in higher dimensions, thus addressing a compelling theoretical question within the context of general relativity and quantum field theories.

Construction and Characteristics

The authors construct these geometrically complex black holes in even spacetime dimensions greater than four ($(n+1) \geq 4$), by extending the vacuum Einstein equations incorporating a negative cosmological constant. The metrics they propose are parameterized by a mass parameter $m$ and rotation parameters $a_i$. Notably, these metrics remain singularity-free under specific conditions outlined in the paper, such as $2|m| < \prod_{i=1}^N |a_i|^{(2N-1)/N}$, contingent on the mass and angular momentum parameters.

By leveraging the Kerr-Schild form, the authors demonstrate the extendibility of their metrics across Killing horizons and illustrate the metric's regularity at spatial infinity through conformal compactification techniques. A noteworthy claim made is the non-existence of curvature singularities, providing stability under a range of mass and rotation conditions.

Implications of Non-Spherical Horizons

The choice of non-spherical horizon geometries allows one to probe deeper into the intricacies of higher-dimensional gravitational dynamics. Specifically, the horizon’s topology potentially influences the nature of Hawking radiation, thermodynamic properties, and the stability of the black holes. Importantly, the discovery corroborates previous theoretical predictions concerning non-spherical black holes, thus enriching the catalogue of known solutions beyond five dimensions.

The paper further discusses causality within these spacetimes, addressing potential breakdowns due to closed timelike curves. The conditions under which stable causality is maintained are explicitly derived, providing a comprehensive understanding of their global structure. These findings give direct implications for the potential formation and evolution of such black holes in scenarios approached by theoretical cosmology and fundamental physics.

Future Directions

This research establishes a foundation for future explorations into asymmetric black hole configurations, prompting questions regarding their potential role in cosmological scenarios and the microscopic structure of spacetime. The work invites further studies into odd-dimensional setups and initial conditions with positive cosmological constants. Additionally, the ramifications of such black hole solutions in holographic theories and their relationship with the dynamics of space-time horizons warrant extensive further exploration.

In conclusion, the paper presents a significant step forward in the exploration of non-trivial horizon geometries in higher-dimensional black holes. Its contributions lie not only in expanding theoretical physics' understanding of black hole horizon dynamics but also in fostering new paths for research in theoretical gravitational physics, fitting into the broader framework of quantum gravity and string theory landscapes.