0599956 - MÚ 2025 RIV DE eng J - Journal Article
Barrientos, José - Cisterna, A. - Hassaine, M. - Oliva, J.
Revisiting Buchdahl transformations: new static and rotating black holes in vacuum, double copy, and hairy extensions.
European Physical Journal C. Roč. 84, č. 10 (2024), č. článku 1011. ISSN 1434-6044. E-ISSN 1434-6052
Institutional support: RVO:67985840
Keywords : black holes * mathematical transformations * black-hole spacetimes
OECD category: Pure mathematics
Impact factor: 4.2, year: 2023 ; AIS: 1.117, rok: 2023
Method of publishing: Open access
Result website:
https://doi.org/10.1140/epjc/s10052-024-13383-4DOI: https://doi.org/10.1140/epjc/s10052-024-13383-4

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.
Permanent Link: https://hdl.handle.net/11104/0357353