Abstract
An affirmative answer is given to a conjecture of Myers concerning the existence of 5-dimensional regular static vacuum solutions that balance an infinite number of black holes, which have Kasner asymptotics. A variety of examples are constructed, having different combinations of ring S1 × S2 and sphere S3 cross-sectional horizon topologies. Furthermore, we show the existence of 5-dimensional vacuum solitons with Kasner asymptotics. These are regular static space-periodic vacuum spacetimes devoid of black holes. Consequently, we also obtain new examples of complete Riemannian manifolds of nonnegative Ricci curvature in dimension 4, and zero Ricci curvature in dimension 5, having arbitrarily large as well as infinite second Betti number.
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Khuri, M., Weinstein, G. & Yamada, S. 5-dimensional space-periodic solutions of the static vacuum Einstein equations. J. High Energ. Phys. 2020, 2 (2020). https://doi.org/10.1007/JHEP12(2020)002
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DOI: https://doi.org/10.1007/JHEP12(2020)002