Figure 1: The BKL billiard of pure four-dimensional gravity. The figure represents the billiard region
projected onto the hyperbolic plane. The particle geodesic is confined to the fundamental region
enclosed by the three walls and , as
indicated by the numbering in the figure. The two symmetry walls and
intersect at an angle of , while the gravity wall intersects, respectively, at angles
and with the symmetry walls and . The particle has no direction
of escape so the dynamics is chaotic.
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