Massive Particle Motion Around Horndeski Black Holes

TL;DR

This paper analyzes the motion of massive particles around Horndeski black holes, deriving analytical solutions and applying perihelion precession to constrain scalar-tensor gravity theories.

Contribution

It provides the first detailed analytical study of particle orbits in Horndeski black hole spacetimes and links orbital precession to observational constraints.

Findings

Analytical solutions for particle trajectories using elliptic functions

Classification of possible orbits around Horndeski black holes

Constraints on scalar field coupling from perihelion precession data

Abstract

The time-like structure of the four-dimensional asymptotically flat Horndeski black holes is studied in detail. Focusing on the motion of massive neutral test particles, we construct the corresponding effective potential and classify the admissible types of orbits. The equations of motion are solved analytically, yielding trajectories expressed in terms of Weierstrass elliptic functions and elementary functions. As an application, we compute the perihelion precession as a classical test of gravity within the Solar System and use it to place observational constraints on the coupling parameter between the scalar field and gravity.