Scattering map for two black holes

Details Scattering map for two black holes Scattering map for two black holes

1999-10-25

arxiv.org/abs/gr-qc/9910090v1

Phys.Rev. E62 (2000) 4784-4791

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 5 figures, uses REVTEX

Scientific paper

10.1103/PhysRevE.62.4784

We study the motion of light in the gravitational field of two Schwarzschild black holes, making the approximation that they are far apart, so that the motion of light rays in the neighborhood of one black hole can be considered to be the result of the action of each black hole separately. Using this approximation, the dynamics is reduced to a 2-dimensional map, which we study both numerically and analytically. The map is found to be chaotic, with a fractal basin boundary separating the possible outcomes of the orbits (escape or falling into one of the black holes). In the limit of large separation distances, the basin boundary becomes a self-similar Cantor set, and we find that the box-counting dimension decays slowly with the separation distance, following a logarithmic decay law.

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