A supersymmetric black lens (1408.6083v2)

Abstract: We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens space topology L(2,1). It is the first example of an asymptotically flat black hole with lens space topology. The solution is characterised by a charge, two angular momenta and a magnetic flux through a non-contractible disc region ending on the horizon, with one constraint relating these.

• The paper introduces a novel supersymmetric black lens solution with L(2,1) horizon topology in five-dimensional minimal supergravity.
• It employs harmonic functions and Gibbons-Hawking spaces to construct a regular, asymptotically flat metric that avoids singularities.
• The study challenges black hole uniqueness by showing that non-spherical topologies can exist while preserving supersymmetry and physical viability.

Supersymmetric Black Lens in Five-Dimensional Supergravity

The paper by Kunduri and Lucietti posits the existence of a supersymmetric, asymptotically flat, black hole solution in five-dimensional minimal supergravity characterized by a lens space topology. This represents a significant development in the theoretical understanding of higher-dimensional black holes, challenging the traditional view that such solutions must have spherical horizon topology.

Key Methodologies and Results

The authors construct a black lens solution with horizon topology $L(2,1)$ using the framework of Gibbons-Hawking spaces, which underpins the metric formulation for this supergravity model. They employ harmonic functions $H, K, L,$ and $M$ as core components in formulating the metric function $f$ and the 1-form $\omega$, yielding a solution specifically to five-dimensional minimal supergravity.

A remarkable aspect of their approach lies in demonstrating the regularity of the solution near the centers $r = 0$ and $r = r_1$, contending these correspond to an event horizon and a smooth timelike point, respectively. By choosing appropriate constants, they establish asymptotic flatness and avoid singularity, ensuring the solution is physically viable.

The black lens is characterized by three parameters, subject to constraints imposed to guarantee regularity and the asymptotic flatness of the spacetime. The analysis reveals a constraint involving angular momenta and magnetic flux, demonstrating compatibility with supersymmetry while ensuring the absence of closed timelike curves in the outer communication region.

Implications of the Study

This work broadens the landscape of possible black hole topologies within higher-dimensional gravitational theories, particularly in five-dimensional contexts. The existence of lens space topology alongside previously known ring solutions implies a potential reconsideration of black hole uniqueness theorems in dimensions greater than four.

The paper hints at potential implications for string theory entropy calculations, a significant intersection of string theory with black hole physics, where classical gravitational solutions can offer insights into microscopic theory predictions.

Speculations and Future Directions

The existence of non-spherical horizon topologies may prompt further exploration into non-extremal solutions, potentially elucidating new classes of supergravity solutions with gravitational waves or extended objects. While the paper focuses on supersymmetric solutions, investigations into non-supersymmetric configurations could enrich the understanding of black hole solutions under minimal supergravity and wider theories of quantum gravity.

The authors acknowledge the possibility of other black lens solutions under different charges and mass distributions, suggesting fertile ground for further research in higher-dimensional black hole physics. Continued advancements could enhance applications linking gravitational lensing phenomena with quantum field theoretical models, reinforcing the transdisciplinary connections between gravitational physics and quantum theory.