Abstract
We probe D1D5 micro-state geometries with massless particles, waves and strings. To this end, we study geodetic motion, Klein-Gordon equation and string scattering in the resulting gravitational background. Due to the reduced rotational symmetry, even in the simple case of a circular fuzzball, the system cannot be integrated elementarily. Yet, for motion in the plane of the string profile or in the orthogonal plane to it, one can compute the deflection angle or the phase shift and identify the critical impact parameter, at which even a massless probe is captured by the fuzzball if its internal momentum is properly tuned. We find agreement among the three approaches, thus giving further support to the fuzzball proposal at the dynamical level.
Highlights
Hole states in five and four dimensions respectively [8–12]
The stringy micro-states can be counted exactly and put in correspondence with regular geometries associated to the U-duality equivalent 2-charge system realised in terms of a bound-state of D1- and D5-branes
In this paper we explore the fuzzball geometries by scattering massless closed string states from the D1/D5 brane system
Summary
Where a line, respectively a dot, denote a Neumann (N), respectively a Dirichlet (D), direction. We will use the coordinates (t, z) for the two NN directions (X0, X5), x = In order to compute the integrals, it is convenient to change coordinates and set x1 + ix2 = ρ2 + a2 sin θeiφ , x3 + ix4 = ρ cos θeiψ (2.8). In this coordinates the metric of a circular D1/D5 fuzzball reads ds2fuzz = H−1 −(dt + ωφdφ)2 + (dz + ωψdψ)[2]. It has been shown that, despite the apparent singularities of Hi along the string profile, the metrics defined in this way are regular everywhere
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