威尼斯人娱乐场

Abstract

We demonstrate that the photon sphere plays a surprising role in theholography for small AdS-Schwarzschild black holes. A precise formula isderived to show how a black hole amplifies or attenuates an oscillatincsource dual to boundary operators across the bulk. We estimate the quasinormal modes of small black holes at large angular momenta l. The lowesimode matches the phase transition for the massless scalar fields and the nulgeodesics, which are identified with the short-lived excitations of the blackhole at large l. This sharpens the conjecture by Hashimoto that the photorsphere seen by a boundary observer is the spatial Fourier transform of theresponse function. The conjecture agrees excellently with numerics aftercertain long-lived excitations -- associated with geodesics connectincboundary points, predicted by Festuccia and Liu -- are removed from theresponse, which is then controlled by the short-lived excitations of the blackhole.