Chaos around a black hole

LUCA BOMBELLI; ESTEBAN CALZETTA

CLASSICAL AND QUANTUM GRAVITY

IOP PUBLISHING LTD

Año: 1992 vol. 9 p. 2573 - 2599

0264-9381

The authors apply the Melnikov method for identifying chaos in near integrable systems to relativistic particle motion around a Schwarzschild black hole. They start by giving a self-contained introduction to the Melnikov method together with some relevant background on dynamical systems. Then they show that a relativistic particle was unstable circular orbits around a Schwarzschild black hole, and that each one of these gives rise to a homoclinic orbit in phase space, which tends to the unstable one for t to +or- infinity . Finally, the authors use the Melnikov method to conclude that, under most periodic perturbations of the black-hole metric, the homoclinic orbit becomes chaotic.