Abstract
Tidal effects in capped geometries computed in previous literature display no dynamics along internal (toroidal) directions. However, the dual CFT picture suggests otherwise. To resolve this tension, we consider a set of infalling null geodesics in a family of black hole microstate geometries with a smooth cap at the bottom of a long BTZ-like throat. Using the Penrose limit, we show that a string following one of these geodesics feels tidal stresses along all spatial directions, including internal toroidal directions. We find that the tidal effects along the internal directions are of the same order of magnitude as those along other, non-internal, directions. Furthermore, these tidal effects oscillate as a function of the distance from the cap — as a string falls down the throat it alternately experiences compression and stretching. We explain some physical properties of this oscillation and comment on the dual CFT interpretation.
Highlights
Background geometryConsider the line element of (1, 0, n) superstrata in the string frame [3, 4, 13]ds2 = Π 1 ds2 + Q1 ds2, Λ6 Q5 T 4 (2.1)where ds26 is the six dimensional metric in the Einstein frame and ds2T 4 = δab dza dzb denotes the metric on the four-torus T 4, which we take to be flat
Using the Penrose limit, we show that a string following one of these geodesics feels tidal stresses along all spatial directions, including internal toroidal directions
This is just a rewriting of the initial metric using a set of null geodesics, this form is convenient when considering the Penrose limit to focus on the neighbourhood of a particular null geodesic, which in turn allows us to extract the tidal forces felt by a string as it moves along the chosen null trajectory
Summary
We describe a family of capped and horizonless geometries, called (1, 0, n) superstrata which have the same charges as the D1-D5-P black hole. The bottom of the throat is the region that contains most of the microstructure — the bump functions have maxima/minima and the superstratum significantly differs from an ordinary black hole. For the latter the throat is infinitely long, while for the superstratum the length of the throat is governed by the ratio b/a, which we usually take to be large in order to approximate the √. In the region r n a, (2.3a) smoothly caps off
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