TY - JOUR

T1 - THE GEOMETRY AND TOPOLOGY OF STATIONARY MULTIAXISYMMETRIC VACUUM BLACK HOLES IN HIGHER DIMENSIONS

AU - Kakkat, Vishnu

AU - Khuri, Marcus

AU - Rainone, Jordan

AU - Weinstein, Gilbert

N1 - Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open

PY - 2023

Y1 - 2023

N2 - Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in (n+3)-dimensional spacetimes admitting the isometry group R×U(1)n, with Kaluza–Klein asymptotics for n ≥ 3. This is equivalent to establishing existence and uniqueness for singular harmonic maps φ: R3 \ Γ → SL(n + 1,R)/SO(n + 1) with prescribed blow-up along Γ, a subset of the z-axis in R3. We also analyze the topology of the domain of outer communication for these spacetimes, by developing an appropriate generalization of the plumbing construction used in the lower-dimensional case. Furthermore, we provide a counterexample to a conjecture of Hollands–Ishibashi concerning the topological classification of the domain of outer communication.

AB - Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in (n+3)-dimensional spacetimes admitting the isometry group R×U(1)n, with Kaluza–Klein asymptotics for n ≥ 3. This is equivalent to establishing existence and uniqueness for singular harmonic maps φ: R3 \ Γ → SL(n + 1,R)/SO(n + 1) with prescribed blow-up along Γ, a subset of the z-axis in R3. We also analyze the topology of the domain of outer communication for these spacetimes, by developing an appropriate generalization of the plumbing construction used in the lower-dimensional case. Furthermore, we provide a counterexample to a conjecture of Hollands–Ishibashi concerning the topological classification of the domain of outer communication.

KW - black holes

KW - domain of outer communication

KW - stationary solutions

UR - http://www.scopus.com/inward/record.url?scp=85158907238&partnerID=8YFLogxK

U2 - 10.2140/pjm.2023.322.59

DO - 10.2140/pjm.2023.322.59

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AN - SCOPUS:85158907238

SN - 0030-8730

VL - 322

SP - 59

EP - 97

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -