https://doi.org/10.1140/epjc/s10052-024-12822-6
Regular Article - Theoretical Physics
Black hole no-hair theorem for self-gravitating time-dependent spherically symmetric multiple scalar fields
1
Department of Theoretical Physics, Faculty of Physics, Sofia University, 1164, Sofia, Bulgaria
2
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 8, 1113, Sofia, Bulgaria
3
Theoretical Astrophysics, Eberhard Karls University of Tübingen, 72076, Tübingen, Germany
4
INRNE-Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria
b
daniela.doneva@uni-tuebingen.de
Received:
27
March
2024
Accepted:
14
April
2024
Published online:
14
May
2024
We prove under certain weak assumptions a black hole no-hair theorem in spherically symmetric spacetimes for self-gravitating time-dependent multiple scalar fields with an arbitrary target space admitting a Killing field with a non-empty axis and arbitrary non-negative potential invariant under the flow of the Killing field. It is shown that for such configurations the only spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. In due course of the proof we also unveil the intrinsic connection of the time-dependence of the scalar fields with the symmetries of the target space.
© The Author(s) 2024
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