Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship

Abstract: We describe the behavior of 5-dimensional black strings, subject to the Gregory-Laflamme instability. Beyond the linear level, the evolving strings exhibit a rich dynamics, where at intermediate stages the horizon can be described as a sequence of 3-dimensional spherical black holes joined by black string segments. These segments are themselves subject to a Gregory-Laflamme instability, resulting in a self-similar cascade, where ever-smaller satellite black holes form connected by ever-thinner string segments. This behavior is akin to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability. The simulation results imply that the string segments will reach zero radius in finite asymptotic time, whence the classical space-time terminates in a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship.

• The paper demonstrates that the nonlinear evolution of 5D black strings via the Gregory-Laflamme instability leads to a cascading formation of satellite black holes.
• It employs advanced numerical methods, including fourth-order finite differencing and adaptive mesh refinement, to effectively capture small-scale dynamics.
• The findings challenge cosmic censorship by linking gravitational instabilities with fluid dynamics analogies and higher entropy configurations.

Analysis of Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship

The paper "Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship" by Lehner and Pretorius contributes to the ongoing study of higher-dimensional black hole analogues by exploring the dynamic instability of five-dimensional black strings influenced by the Gregory-Laflamme (GL) instability. Specific focus is placed on the nonlinear evolution of these black strings beyond the linear perturbation phase, leading to a structure reminiscent of fluid flow instabilities such as the Rayleigh-Plateau instability.

In their exploration of five-dimensional spacetimes, the authors extend the known GL instability to display a self-similar cascade of satellite black holes interconnected by black string segments. As these segments undergo further GL instabilities, they diminish to zero radius over finite asymptotic time, culminating in the emergence of a naked singularity. This process, fundamentally violating cosmic censorship conjectures, does not demand finely-tuned initial conditions, suggesting a more inherent feature of five-dimensional gravitational dynamics.

The paper bolsters its theoretical findings with numerical simulations performed using a generalized harmonic formulation of Einstein's field equations in five-dimensional spacetimes. Surpassing previous studies that ran into computational limits before thoroughly watching the instability evolve, Lehner and Pretorius manage to depict a clear progression toward singularity. Their numerical methods included fourth-order finite differencing and adaptive mesh refinement, enabling them to explore smaller scale dynamics effectively.

Strong numerical outcomes are particularly noteworthy. The integrated apparent horizon (AH) areas calculated show significant increases, nearly analogous to higher entropies emerging from five-dimensional black hole end-states. The authors decisively link their simulations to earlier entropy-based conjectures by Gregory and others, reaffirming the expectation of higher entropy configurations resulting from the breakdown of longer interconnected black string segments. These findings add substantial weight to the idea that entropy considerations drive the transition from uniform black strings to disconnected spherical black holes in higher dimensions.

The work posits various implications for the study of higher-dimensional gravity, quantum gravity theory, and the fluid-gravity correspondence. The established analogy with fluid dynamics, specifically with low viscosity systems, ties together gravitational instabilities with paradigms typically studied within fluid mechanics domains. This broader fluid-horizon analogy opens the door to more cross-disciplinary methods within theoretical physics, leveraging insights from one domain to elucidate behaviors in another.

Future research could build on these results to further examine how quantum effects might address the naked singularity issue that arises from this classical analysis. Additionally, extending these methodologies to other spacetime dimensionalities and configurations, including the impacts of angular momentum, could provide clearer insights into the wider landscape of stability and cosmic censorship within higher dimensional physics.

Overall, this study scrutinizes the intricate dynamics of an unstable five-dimensional black string and its evolutionary path, challenging traditional perceptions of cosmic censorship and advancing the understanding of higher dimensional gravitational phenomena. Such research paves the way for further theoretical exploration and numerical validation of complex relativistic systems.