https://doi.org/10.1140/epjc/s10052-025-13948-x
Regular Article - Theoretical Physics
Geodesic motion of test particles around the scalar hairy black holes with asymmetric vacua
School of Science, Jiangsu University of Science and Technology, 212100, Zhenjiang, Jiangsu, China
Received:
10
November
2024
Accepted:
15
February
2025
Published online:
24
March
2025
An asymptotically flat hairy black hole (HBH) can exhibit distinct characteristics when compared to the Schwarzschild black hole, due to the evasion of no-hair theorem by minimally coupling the Einstein gravity with a scalar potential which possesses asymmetric vacua, i.e, a false vacuum 
and a true vacuum 
. In this paper, we investigate the geodesic motion of both massive test particles and photons in the vicinity of HBH with 
and 
by analyzing their effective potentials derived from the geodesic equation. By fixing 
, the effective potential of a massive test particle increases monotonically when its angular momentum L is very small. When L increases to a critical value, the effective potential possesses an inflection point which is known as the innermost stable circular orbit (ISCO), where the test particle can still remain stable in a circular orbit with a minimal radius without being absorbed by the HBH or fleeing to infinity. Beyond the critical value of L, the effective potential possesses a local minimum and a local maximum, indicating the existence of unstable and stable circular orbits, respectively. Moreover, the HBH possesses an unstable photon sphere but its location slightly deviates from the Schwarzschild black hole. The trajectories of null geodesics in the vicinity of HBH can also be classified into three types, which are the direct, lensing, and photon sphere, based on the deflection angle of light, but the values of impact parameters can vary significantly than the Schwarzschild black hole.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
