Time-periodic Einstein-Klein-Gordon bifurcations of Kerr. (English) Zbl 1381.83008
Authors’ abstract: We construct one-parameter families of solutions to the Einstein-Klein-Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. An immediate corollary is that for these Klein-Gordon masses, the Kerr family is not asymptotically stable as a solution to the Einstein-Klein-Gordon equations.
Reviewer: Anthony D. Osborne (Keele)
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C57 | Black holes |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 35L05 | Wave equation |
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