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

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.

arXiv comment34 pages, 5 figures; to match the published version which combines this number and arXiv:1509.07954

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