# Implementaci\'on computacional para el estudio de part\'iculas con esp\'in en agujeros negros rotantes modificados cu\'anticamente

## TL;DR

This paper presents a computational tool in Mathematica for analyzing the motion of spinning test particles around quantum-improved rotating black holes, exploring how quantum and geometric parameters influence particle orbits.

## Contribution

The work introduces a novel computational implementation that calculates and visualizes test particle trajectories with spin in quantum-modified rotating black hole spacetimes.

## Key findings

- Results align with classical Kerr and Schwarzschild black hole studies.
- The program determines the maximum physically possible spin of test particles.
- Quantum parameters significantly affect particle orbit characteristics.

## Abstract

The trajectories of test particles with spin orbiting a black hole depend on the geometry of space-time and the intrinsic physical characteristics of the test particles. In this work the motion of test particles with spin on the innermost stable circular orbit of a quantum improved rotating black hole is studied. A computational implementation is presented through the Mathematica program, which can calculate and graph the radius, angular momentum and energy as a function of the spin of the test particles and for various geometric parameters of the rotating black hole, as they are the spin $a$ and the mass $M$ of the rotating black hole and the quantum parameters $\gamma$ and $\omega$. Additionally, the program calculates the maximum spin physically possible for the test particles. At the end, some results given by the program are discussed and it is shown that these are consistent with those previously reported, both for the classical black holes of Schwarzschild and Kerr and for the quantum improved ones.