Orbits of Massive Particles in a Spherically Symmetric Gravitational Field in View of Cosmological Constant

TL;DR

This paper theoretically analyzes the trajectories of massive particles in a spherically symmetric gravitational field considering the cosmological constant, classifying possible paths and estimating the upper limit of negative b4 from galaxy rotation data.

Contribution

It introduces a classification scheme for particle trajectories in the Kf6ttler metric considering b4, including solutions via Puiseux series expansion, and estimates the negative b4 limit from galaxy rotation curves.

Findings

Classified trajectories for positive and negative b4 values.

Derived solutions using Puiseux series expansion.

Estimated upper limit of negative b4 from galaxy rotation data.

Abstract

In this paper we present the results of a theoretical study of the trajectories of massive particles in the K\"ottler metric in view of the cosmological constant {\Lambda}. For both negative and positive signs of {\Lambda} a classification of trajectories is proposed, with entries based on different solutions of the trajectory equation, obtained by the expansion of the corresponding algebraic curve in Puiseux series. We also provide some specific types of trajectories which correspond to different values of the cosmological constant. In the case of negative values of the cosmological constant its upper limit is estimated from the galaxy rotation curves