Phantom hairy black holes and wormholes in Einstein-bumblebee gravity

Chikun Ding; Changqing Liu; Yuehua Xiao; Jun Chen

doi:10.1140/epjc/s10052-025-13815-9

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 73
https://doi.org/10.1140/epjc/s10052-025-13815-9

Regular Article - Theoretical Physics

Phantom hairy black holes and wormholes in Einstein-bumblebee gravity

Chikun Ding¹^,2^a, Changqing Liu¹, Yuehua Xiao¹ and Jun Chen¹

¹ Department of Physics, Huaihua University, 418008, Huaihua, People’s Republic of China
² Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, 410081, Changsha, Hunan, People’s Republic of China

^a dingchikun@163.com

Received: 21 October 2024
Accepted: 11 January 2025
Published online: 24 January 2025

Abstract

In this paper we study Einstein-bumblebee gravity theory minimally coupled with external matter – a phantom/non-phantom (conventional) scalar field, and derive a series of hairy solutions – bumblebee-phantom (BP) and BP-dS/AdS black hole solutions, regular Ellis-bumblebee-phantom (EBP) and BP-AdS wormholes, etc. We first find that the Lorentz violation (LV) effect can change the so-called black hole no-hair theorem and these scalar fields can give a hair to a black hole. If LV coupling constant $ℓ > - 1$ $\ell >-1$ , the phantom field is admissible and the conventional scalar field is forbidden; if $ℓ < - 1$ $\ell <-1$ , the phantom field is forbidden and the conventional scalar field is admissible. By defining the Killing potential $ω^{ab}$ $\omega ^{ab}$ , we study the Smarr formula and the first law for the BP black hole, find that the appearance of LV can improve the structure of these phantom hairy black holes – the conventional Smarr formula and the first law of black hole thermodynamics still hold; but for no LV case, i.e., the regular phantom black hole reported in (Phys Rev Lett 96:251101), the first law cannot be constructed at all. We also show there still exists a stable circular orbit around the BP black hole. When the bumblebee potential is linear, we find that the phantom potential and the Lagrange-multiplier $λ$ $\lambda$ behave as a cosmological constant $Λ$ $\Lambda$ .

© The Author(s) 2025

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