TY - JOUR

T1 - Time-Periodic Einstein–Klein–Gordon Bifurcations of Kerr

AU - Chodosh, Otis

AU - Shlapentokh-Rothman, Yakov

N1 - Funding Information:
Acknowledgements. OC was supported by an EPSRC Programme Grant entitled Singularities of Geometric Partial Differential Equations, Number EP/K00865X/1 during part of the time this work was completed and is grateful to Simon Brendle for his encouragement concerning this work. YS acknowledges support from the NSF Postdoctoral Research Fellowship under Award No. 1502569, and thanks Igor Rodnianski and Mihalis Dafermos for stimulating conversations about the paper. Finally, we are grateful to the referees whose many suggestions greatly improved the exposition and organization of the paper.
Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-017-2998-3

DO - 10.1007/s00220-017-2998-3

M3 - Article

AN - SCOPUS:85030672662

SN - 0010-3616

VL - 356

SP - 1155

EP - 1250

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -