https://doi.org/10.1140/epjc/s10052-024-12450-0
Regular Article - Theoretical Physics
New anisotropic Gauss–Bonnet black holes in five dimensions at the critical point
1
Department of Physics, School of Science, East China University of Technology, 330013, Nanchang, Jiangxi, People’s Republic of China
2
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China
Received:
3
November
2023
Accepted:
12
January
2024
Published online:
25
January
2024
We obtain new vacuum static black hole solutions with anisotropic horizons in Einstein–Gauss–Bonnet gravity with a negative cosmological constant in five dimensions. The translational invariance along one direction on the 3-dimensional horizon cross section is broken. The Gauss–Bonnet coupling is at the critical point where there is one single AdS vacuum. These solutions does not appear in the form of a warped product, i.e. they lack a common warping factor, and the metric contains 2 arbitrary functions, h(r) of the radial coordinate r and H(y) of the horizon coordinate y – some degeneracy in the metric. The nontrivial horizon and the degeneracy may be closely related to the critical value of
. We introduce the process of obtaining the solutions and some of their properties, and also prove a uniqueness theorem for the case when there is a common warping factor for the rest two directions.
© The Author(s) 2024
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