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

Vishnu Kakkat, Marcus Khuri, Jordan Rainone, Gilbert Weinstein

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)59-97
Number of pages39
JournalPacific Journal of Mathematics
Volume322
Issue number1
DOIs
StatePublished - 2023

Keywords

  • black holes
  • domain of outer communication
  • stationary solutions

All Science Journal Classification (ASJC) codes

  • General Mathematics

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