L Bombelli and E Calzetta 1992 Class. Quantum Grav. 9 2573 doi:10.1088/0264-9381/9/12/004
L Bombelli and E Calzetta
Show affiliationsThe 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.
04.70.-s Physics of black holes
37D45 Strange attractors, chaotic dynamics
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
Issue 12 (December 1992)
L Bombelli and E Calzetta 1992 Class. Quantum Grav. 9 2573
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