https://doi.org/10.1140/epjc/s10052-024-13383-4
Regular Article
Revisiting Buchdahl transformations: new static and rotating black holes in vacuum, double copy, and hairy extensions
1
Sede Esmeralda, Universidad de Tarapacá, Avenida Luis Emilio Recabarren 2477, Iquique, Chile
2
Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic
3
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00, Praha 8, Czech Republic
4
Instituto de Matemáticas, Universidad de Talca, Casilla 747, Talca, Chile
5
Departamento de Física, Universidad de Concepción, Casilla, 160-C, Concepción, Chile
a
jbarrientos@academicos.uta.cl
Received:
8
August
2024
Accepted:
17
September
2024
Published online:
7
October
2024
This paper investigates Buchdahl transformations within the framework of Einstein and Einstein-Scalar theories. Specifically, we establish that the recently proposed Schwarzschild–Levi-Civita spacetime can be obtained by means of a Buchdahl transformation of the Schwarschild metric along the spacelike Killing vector. The study extends Buchdahl’s original theorem by combining it with the Kerr–Schild representation. In doing so, we construct new vacuum-rotating black holes in higher dimensions which can be viewed as the Levi-Civita extensions of the Myers–Perry geometries. Furthermore, it demonstrates that the double copy scheme within these new generated geometries still holds, providing an example of an algebraically general double copy framework. In the context of the Einstein-Scalar system, the paper extends the corresponding Buchdahl theorem to scenarios where a static vacuum seed configuration, transformed with respect to a spacelike Killing vector, generates a hairy black hole spacetime. We analyze the geometrical features of these spacetimes and investigate how a change of frame, via conformal transformations, leads to a new family of black hole spacetimes within the Einstein-Conformal-Scalar system.
© The Author(s) 2024
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