Geodesic Motion in Schwarzschild Spacetime Surrounded by Quintessence

TL;DR

This paper analyzes the motion of particles around a Schwarzschild black hole influenced by quintessence, revealing how the quintessence parameter affects orbit structures and geodesic divergence.

Contribution

It provides a detailed analytical and numerical study of geodesic structures in Schwarzschild spacetime with quintessence, highlighting new orbit types and divergence effects.

Findings

Existence of various non-radial orbits including stable and unstable circular orbits.

No bound orbits for radial geodesics.

Quintessence enhances divergence of neighboring geodesics.

Abstract

We study the time-like geodesic congruences, in the space-time geometry of a Schwarzschild black hole surrounded by quintessence. The nature of effective potential along with the structure of the possible orbits for test particles in view of the different values of quintessence parameter are analysed in detail. %wherever possible it is done analytically otherwise numerically. An increase in quintessence parameter is seen to set the particles from farther distance into motion around black hole. The effect of quintessence parameter is investigated analytically wherever possible otherwise we perform the numerical analysis to probe the structure of possible orbits. It is observed that there exist a number of different possible orbits for a test particle in case of non-radial geodesics, such as circular (stable as well as unstable) bound orbits, radially plunge and fly-by orbits, whereas no bound orbits exist in case of radial geodesics. Using the geodesic deviation equations, we obtain the corresponding deviation vector and find that the quintessence assists the divergence of neighbouring geodesics in both the radial and transverse directions.