Geodesic motion of test particles in Korkina-Grigoryev metric

TL;DR

This paper analyzes the geodesic structure of the Korkina-Grigoryev spacetime, a scalar field extension of Schwarzschild geometry, revealing how charge affects particle orbits and stability.

Contribution

It introduces the geodesic analysis of the Korkina-Grigoryev metric, highlighting the influence of scalar charge on particle motion and orbit stability.

Findings

Identified conditions for finite particle motion based on angular momentum and scalar charge.

Determined radii and energies of stable and unstable circular orbits.

Compared effective potential curves across different spacetime metrics, showing orbit stability loss with increasing charge.

Abstract

We study the geodesic structure of the Korkina-Grigoryev spacetime. The corresponding metric is a generalization of the Schwarzschild geometry to the case involving a massless scalar field. We investigate the relation between the angular momentum of the test particle and the charge of the field, which determines the shape of the effective-potential curves. The ratio for angular momentum of the particle, the charge of the scalar field and the dimensionless spatial parameter is found, under which the finite motion of particles occurs. From the behavior of the potential curves the radii of both stable and unstable circular orbits around a black hole are found, as well as the corresponding energies of the test particles. The effective-potential curves for the Korkina-Grigoryev, the Schwarzschild and the Reissner-Nordstrom fields are compared. It is shown, that in the case of the Korkina-Grigoryev metric the stable orbits eventually vanish with increasing charge.