Precessing and periodic orbits around hairy black holes in Horndeski’s Theory

Abstract

We investigate the dynamics of neutral timelike particles around a hairy black hole in Horndeski’s theory, which is characterized by a coupling parameter with the dimension of length. With deriving the particles’ relativistic periastron precessions, a preliminary bound on the hairy black hole is obtained by using the result of the S2 star’s precession with GRAVITY. It is tighter than the previous result constrained by the shadow size from EHT observations of M87* by about 3–4 orders of magnitude. We also analyse the particles’ periodic motions around the hole in the strong gravitational field. It clearly shows that small variations in the coupling parameter can make the neutral particles’ motions back and forth from the quasi-periodic orbits to the periodic orbits or no bound orbit. Our present work might provide hints for distinguishing the hairy black hole in Horndeski’s theory from the classical hole by using the particles’ dynamics in the strong gravitational field.

Influences of tilted thin accretion disks on the observational appearance of hairy black holes in Horndeski gravity

“…The spacetime described by the spherically symmetric Horndeski metric (2.1) is asymptotically flat and degenerates to the classical Schwarzschild case when the scalar hair is absent (h → 0). Interestingly, by examining the variation of the lapse function (2.3) with radius r, previous studies have confirmed that the event horizon r + of the hairy BH is located at 2M when the scalar hair parameter satisfies the condition h ≥ −2 [28,65,[70][71][72].…”

“…Note that the features of the strong gravitational field of Horndeski BHs can be revealed by examining the motions of massive particles in the vicinity of the BH. Following this line of thought, Lin and Deng simulated a series of periodic and quasiperiodic orbits with different leaves, whirl numbers, and precession around the hairy BH by the elaborate selection of the particles' energy and angular momentum [70]. Their study obtained a preliminary bound on the hairy BH based on matching particles' relativistic periastron precession with that of the S2 star reported by the GRAVITY Collaboration, which is about 3 − 4 orders of magnitude tighter JCAP04(2024)089 than the constraint obtained by the shadow observations of M87 * .…”

“…In Boyer-Lindquist coordinates x µ = (t, r, θ, φ), the static spherically symmetric BH with scalar hair in Horndeski gravity can be found in [28,65,[68][69][70] as…”

Properties of Spherically Symmetric Black Holes in the Generalized Brans–Dicke Modified Gravitational Theory

“…Some works on the circular orbits of particles can be seen in Refs. [36,[63][64][65][66][67], e.g., the issues on the spherical photon orbits around a Kerr BH [63], the dynamics of charged particles moving around Kerr BH with inductive charge and external magnetic field [65], the equivalence between two charged black holes in dynamics of orbits outside the event horizons [36], and the precessing and periodic orbits around hairy black holes in Horndeskis theory [67], were discussed. These studies can be utilized to distinguish different BHs, investigate the properties of spacetime in strong gravitational fields, and subsequently test theories of gravitational interaction.…”