Geodesic Motion of Test Particles around the Scalar Hairy Black Holes with Asymmetric Vacua

Abstract

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 $(\varphi =0)$ and a true vacuum $(\varphi ={\varphi }_1)$. In this paper, we investigate the geodesic motion of both massive test particles and photons in the vicinity of HBH with ${\varphi }_1=0.5$ and ${\varphi }_1=1.0$ by analyzing their effective potentials derived from the geodesic equation. By fixing ${\varphi }_1$, 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 of 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.

11 pages with total 11 figures

References in corpus (21)

• Black Hole Shadows, Photon Rings, and Lensing Rings
• Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
• Geodesic motion in Euclidean Schwarzschild geometry
• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Analytic solutions for the motion of spinning particles near spherically symmetric black holes and exotic compact objects
• Motion of charged particles around a magnetized/electrified black hole
• Kerr Geodesics in Terms of Weierstrass Elliptic Functions
• Null and time-like geodesics in Kerr-Newman black hole exterior
• Precessing and periodic timelike orbits and their potential applications in Einsteinian cubic gravity
• Tidal Love numbers and approximate universal relations for fermion soliton stars
• Fermion Soliton Stars with Asymmetric Vacua
• Black Holes with Scalar Hair in Three Dimensions
• Scalar Hairy Black Holes with Inverted Mexican Hat Potential
• Motion of spinning particles around a polymer black hole in loop quantum gravity
• Homoclinic orbits in Kerr-Newman black holes
• The simplest model of a scalarized black hole in the Einstein-Klein-Gordon theory
• Charged hairy black holes in the gauged Einstein-Friedberg-Lee-Sirlin model
• Hypocycloid motion in the Melvin magnetic universe
• Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes
• Gravitating Scalarons with Inverted Higgs Potential
• Probing light scalars with not quite black holes

Cited by in corpus (1)

• Shadow of the Scalar Hairy Black Hole with Inverted Higgs Potential