5-dimensional space-periodic solutions of the static vacuum Einstein equations

Marcus Khuri; Gilbert Weinstein; Sumio Yamada

doi:10.1007/JHEP12(2020)002

5-dimensional space-periodic solutions of the static vacuum Einstein equations

Marcus Khuri, Gilbert Weinstein, Sumio Yamada

Department of Physics

Ariel University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	2
Journal	Journal of High Energy Physics
Volume	2020
Issue number	12
DOIs	https://doi.org/10.1007/JHEP12(2020)002
State	Published - Dec 2020

Keywords

Black Holes
Differential and Algebraic Geometry

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

Access to Document

10.1007/JHEP12(2020)002

Cite this

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title = "5-dimensional space-periodic solutions of the static vacuum Einstein equations",

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.",

keywords = "Black Holes, Differential and Algebraic Geometry",

author = "Marcus Khuri and Gilbert Weinstein and Sumio Yamada",

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year = "2020",

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doi = "10.1007/JHEP12(2020)002",

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AU - Khuri, Marcus

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N2 - 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.

AB - 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.

KW - Black Holes

KW - Differential and Algebraic Geometry

UR - http://www.scopus.com/inward/record.url?scp=85097446826&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2020)002

DO - 10.1007/JHEP12(2020)002

M3 - مقالة

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 12

M1 - 2

ER -

5-dimensional space-periodic solutions of the static vacuum Einstein equations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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