Toroidal Tidal Effects in Microstate Geometries

TL;DR

This paper demonstrates that strings falling into microstate geometries experience significant tidal effects along internal toroidal directions, resolving previous discrepancies between geometric and CFT descriptions by analyzing geodesics and tidal stresses.

Contribution

It reveals that internal toroidal directions in microstate geometries exhibit tidal effects comparable to external directions, using Penrose limits and geodesic analysis to reconcile geometric and CFT perspectives.

Findings

Tidal stresses are present along all spatial directions, including internal toroidal ones.

Tidal effects oscillate as the string approaches the cap, causing alternating compression and stretching.

Tidal effects along internal directions are of the same order as those along other directions.

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.