The slowly rotating near extremal D1–D5 system as a ‘hot tube’

Abstract

The geometry of the D1-D5 system with a small angular momentum j has a long throat ending in a conical defect. We solve the scalar wave equation for low energy quanta in this geometry. The quantum is found to reflect off the end of the throat, and stay trapped in the throat for a long time. The length of the throat for j=1/2 equals n 1 n 5 R, the length of the effective string in the CFT; we also find that at this distance the incident wave becomes nonlinear. Filling the throat with several quanta gives a 'hot tube' which has emission properties similar to those of the near extremal black hole.

(Non)-integrability of geodesics in D-brane backgrounds

“…Thus we conclude that coordinates (6.21) used in [67,68] are essentially the elliptic coordinates up to a minor redefinition of r ′ . We will come back to this feature in section 8.…”

“…Notice that integrability of (6.16) follows from separability of the wave equation in the background (6.1), (6.17), which has been discovered long time ago [34,67]. Let us clarify the relation between variables used in these papers and the elliptic coordinates (3.55), (6.14).…”

“…Moreover, a strong support for the fuzzball picture came from analyzing the properties of these metrics [67], and success of this study was based on separability of the wave equation on a special classes of metrics. In this paper we have been focusing on separability of the HJ equation as necessary condition for integrability of strings, but such separability also implies separability of the wave equation.…”

“…To separate the wave equation in the metric (6.1) with harmonic functions (6.17), one can use the coordinates (r ′ , θ ′ ) which appear naturally if the D1-D5 solution is viewed as an extremal limit of a black hole [34,67,68]:…”

Analyzing the squeezed state generated by a twist deformation

“…A very useful microscopic model for the study of black holes [1,2,3,4,5] has been the D1D5 conformal field theory (CFT) [6]. One makes a bound state of D1 and D5 branes, and the CFT emerges as a description of the low energy dynamics of this bound state.…”