Schwarzschild and Kerr black holes: an approach using Python

Abstract

In the present work, the reader will be able to study the main historical notes about the importance of studying the four models of black holes. Later you will be able to understand how stellar evolution, formation and structure of black holes works by analyzing the components of the Schwarzschild metric, the circumference of the event horizon, the proper distance, the proper time, the event horizon, the photon sphere, the disk accretion, singularity and naked singularity, Einstein ring and Einstein cross for this geometric model. For the Kerr axial symmetry model, the components of the metric that lead to eigentime, eigendistance, particle orbit, event horizon, ergoregion, infinite redshift surface, cosmic censorship will be studied in the case where $ r > 2M$, the static limit, the shadow of a Kerr black hole. A filter for analyzing the profile of a Schwarzschild and Kerr black hole from the European Space Agency was made available. The simulations were created in Python using some special packages for the General Theory of Relativity and are fully included in the appendix for possible consultation. The natural units were also adopted to describe the Schwazrschild and Kerr metrics, both with the metric signature (-, +, +, +).