Aplicação da biblioteca de múltipla precisão na investigação de caos em trajetórias de partículas em torno de buracos negros

Abstract

The motion of massive particles in an external magnetic field around a black hole can be found using the Hamiltonian formalism adapted for General Relativity, with the particle’s proper time serving as the independent variable. The resulting dynamical systems are, in general, non-integrable, opening up the possibility of chaotic motion. It is therefore interesting to develop and apply numerical integration methods which are both efficient and precise for calculating the particle trajectories. The main aim of the work presented in this dissertation is to develop programs which are both fast and highly accurate, with a precision which can be adapted according to the application and needs of the user. To this end, we have implemented a program for integrating differential equations based on the fourth-order Runge-Kutta method, using C++ and the multiple precision library MPFR. The program was compared with equivalent implementations in double precision C and Maple, and showed greater accuracy than the former, while being faster than the latter at the same level of precision. As a physical application, the program was used to investigate chaos in particle trajectories around black holes.