Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes

TL;DR

This paper demonstrates the formation of naked singularities in 5+1 dimensional vacuum Einstein spacetimes through specific solutions derived from higher-dimensional reductions, challenging aspects of cosmic censorship.

Contribution

It provides explicit higher-dimensional solutions showing naked singularity formation, using Kaluza-Klein reduction and self-similar solutions from 4D Einstein-scalar systems, a novel approach in this context.

Findings

Naked singularities can form in 5+1 dimensions without trapped surfaces.

Constructed solutions are based on lifting 4D self-similar Einstein-scalar solutions.

Failed to replicate naked singularities in 4+1 dimensions using similar methods.

Abstract

The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locally flat initial data that contain no trapped surface. We present a class of specific examples with topology $\mathbb{R}^{3+1} \times S^2$. Thanks to the Kaluza-Klein dimensional reduction, these examples are constructed by lifting continuously self-similar solutions of the 4-dimensional Einstein-scalar field system with a negative exponential potential. The latter solutions are obtained by solving a 3-dimensional autonomous system of first-order ordinary differential equations with a combined analytic and numerical approach. Their existence provides a new test-bed for weak cosmic censorship in higher-dimensional gravity. In addition, we point out that a similar attempt of lifting Christodoulou's naked singularity solutions of massless scalar fields fails to capture formation of naked singularities in 4+1 dimensions, due to a diverging Kretschmann scalar in the initial data.