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 language | English |
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Pages (from-to) | 59-97 |
Number of pages | 39 |
Journal | Pacific Journal of Mathematics |
Volume | 322 |
Issue number | 1 |
DOIs | |
State | Published - 2023 |
Keywords
- black holes
- domain of outer communication
- stationary solutions
All Science Journal Classification (ASJC) codes
- General Mathematics