2-charge circular fuzz-balls and their perturbations

TL;DR

This paper investigates perturbations of 2-charge circular fuzz-balls, revealing new long-lived modes, non-zero static tidal Love numbers, and connecting these findings to quantum field theories, with results supported by numerical and analytical methods.

Contribution

It introduces the analysis of perturbations around 2-charge fuzz-balls, discovering long-lived QNMs, non-zero tidal Love numbers, and establishing a link to quantum Seiberg-Witten curves and Liouville CFT.

Findings

Discovery of long-lived QNMs localized inside the photon-sphere.

Identification of non-zero static tidal Love numbers independent of mass and charges.

Validation of results through numerical methods and analytical approximations.

Abstract

We perform a detailed study of perturbations around 2-charge circular fuzz-balls and compare the results with the ones obtained in the case of 'small' BHs. In addition to the photon-sphere modes that govern the prompt ring-down, we find a new branch of long-lived QNMs localised inside the photon-sphere at the (meta)stable minimum of the radial effective potential. The latter are expected to dominate late time signals in the form of 'echoes'. Moreover, contrary to 'small' BHs, some 'static' tidal Love numbers are non-zero and independent of the mass, charges and angular momentum of the fuzz-ball. We rely on the recently established connection between BH or fuzz-ball perturbation theory and quantum Seiberg-Witten curves for N = 2 SYM theories, which in turn are related to Liouville CFT via the AGT correspondence. We test our results against numerical results obtained with Leaver's method of continuous fractions or Breit-Wigner resonance method for direct integration and with the WKB approximation based on geodesic motion. We also exclude rotational super-radiance, due to the absence of an ergo-region, and absorption, due to the absence of a horizon.