Early scrambling and capped BTZ geometries

Abstract

Geodesic probes in certain horizonless microstate geometries experience extreme tidal forces long before reaching the region where these geometries differ significantly from the extremal BTZ black hole. The purpose of this paper is to show that this behavior is a universal feature of all geometries that have a long BTZ throat that terminates in a cap, regardless of the details of this cap. Hence, incoming probes will scramble into the microstate structure before they encounter the region where the charges of the solution are sourced, and the reason for this premature scrambling is the amplification of tiny geometrical deviations by the relativistic speeds of the probes. To illustrate the phenomenon, we construct a new family of smooth horizonless superstratum microstate geometries, dual to D1-D5 CFT states whose momentum charge is carried by excitations on CFT strands of length k. We also show that, in the large-k limit, these new superstrata resemble a blackened supertube solution everywhere except in the near-supertube region. Thus they resolve the singularity caused by the naive back-reaction of modes with non-linear instabilities near evanescent ergosurfaces.

Little strings, long strings, and fuzzballs

“…Both processes require some energy to be supplied. 24 One of the excitations that costs rather little energy is to pry a fundamental string loose from the background. In [67] it was shown that large gauge transformations in the SL(2, R) factor of G mediate processes by which F1 winding charge dissolved as background flux can be transferred to winding string excitations not bound to the cap.…”

“…The fully nonlinear field equations are solved, with the wave profile tuned to avoid singularities and other pathologies such as closed timelike curves. However, it has been shown [24,134] that probes of this geometry experience large tidal forces, an indicator that the large blueshift experienced by the probe will result in processes wellapproximated by the collision of gravitational shockwaves, resulting in a disruption of the delicately tuned superstratum structure. There will be plenty of excitation energy available to transfer angular momentum away from the supertube, causing it to evolve toward the regime where W-branes become light.…”

Holomorphic waves of black hole microstructure

“…Nevertheless, quite a number of physically interesting microstate geometries are ultimately rather simple. Some can be reduced to (2+1)-dimensional backgrounds that are best described as smoothly capped BTZ geometries [2][3][4][5][6][7]. That is, the geometry is asymptotic, at infinity, to AdS 3 .…”

“…In some classes of these geometries, the massless scalar wave equation is even separable [4,[7][8][9]. This has enabled a great deal of analysis of such geometries and an investigation of their possible effects on microstructure [4,10,11,6,7].…”

“…6) where the functions (ω ξ , ω µ , ω χ , ω δ ) are necessarily real. The relationship between the components here and the ansatz used in(3.34) can be easily worked out from dθ + 2ω χ dϕ 1 + 2ω δ dϕ 2 .…”