# Hyperbolic trajectories around Black Holes

## TL;DR

This paper investigates the paths of test particles near Schwarzschild black holes, focusing on hyperbolic trajectories constrained to resemble jet sections, highlighting the role of conserved quantities like energy and angular momentum.

## Contribution

It introduces a study of constrained hyperbolic trajectories around black holes, connecting conserved quantities to specific jet-like particle paths.

## Key findings

- Hyperbolic trajectories are influenced by conserved energy and angular momentum.
- Constrained trajectories resemble sections of astrophysical jets.
- Analysis enhances understanding of particle motion near black holes.

## Abstract

We analyse test particle's trajectories around the geometry of a Schwarzschild black hole. In order to resemble sections of jets in the neighborhood of a black hole, we consider the conserved quantities corresponding to constraints imposed on the trajectories of the test particles, namely conic and hyperboloidic trajectories. As expected, the energy and angular momentum are closely related to the solutions in the non-constrained case.