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Examples of Naked Singularity Formation in Higher-Dimensional Einstein-Vacuum Spacetimes

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, M5S 2E4, Canada

    Xinliang An

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854-8019, USA

    Xinliang An

  3. TianQin Research Center for Gravitational Physics School of Physics and Astronomy, Sun Yat-sen University, Zhuhai, 519082, China

    Xuefeng Zhang

  4. Departments of Physics and Astronomy, Beijing Normal University, Beijing, 100875, China

    Xuefeng Zhang

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  1. Xinliang An
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Correspondence to Xuefeng Zhang.

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Communicated by James A. Isenberg.

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An, X., Zhang, X. Examples of Naked Singularity Formation in Higher-Dimensional Einstein-Vacuum Spacetimes. Ann. Henri Poincaré 19, 619–651 (2018). https://doi.org/10.1007/s00023-017-0631-9

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