Trapping, chaos and averaging in bubbling AdS spaces

A bstract We discuss chaos and ensemble averaging in 1/2 BPS bubbling AdS spaces of Lin, Lunin and Maldacena (LLM) by studying trapped and escaping null geodesics and estimating their decay rates. We find typical chaotic scattering behavior and confirm the Pesin relation between escape rates, Lyapunov exponents and Kolmogorov-Sinai entropy. On the other hand, for geodesics in coarse-grained (grayscale) LLM geometries (which exhibit a naked singularity) chaos is strongly suppressed, which is consistent with orbits and escape rates averaged over microscopic backgrounds. Also the singularities in these grayscale geometries produce an attractive potential and have some similarities to black hole throats trapping geodesics for a long time. Overall, averaging over the ensembles of LLM geometries brings us closer toward the typical behavior of geodesics in black hole backgrounds, but some important differences remain, in particular the existence of a threshold timescale when the averaging fails.