Mihailo Cubrovic
Ensemble averaging in LLM geometriesAbstract
We consider dynamics of ensembles of geodesics in Lin-Lunin-Maldacena (LLM) geometries, first black and white and then grayscale (coarse-grained). We find that ensemble averaging over geodesics converges to an "average" geodesic which on long timescales coincides with the geodesic in grayscale geometries. The same conclusion holds accordingly also for the two-point functions of the dual CFT in the eikonal regime. We then construct a black hole geometry by encircling the singularity of the grayscale LLM solution with a thermal horizon and find that the geodesics and two-point functions in this background are obtained in the first approximation simply by compactifying the ensemble-aberaged results on the thermal circle. All of this suggests that we might understand black holes as averages over microstate solutions
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