Radiation from the non-extremal fuzzball

TL;DR

<3-5 sentence high-level summary>The paper investigates non-extremal fuzzball geometries in the D1-D5 system and shows that their classical ergoregion-type instabilities reproduce Hawking radiation when analyzed via the dual D1-D5 CFT. By matching the semiclassical Hawking emission rate to a CFT emission vertex V(l), the authors fix the CFT normalization and then demonstrate that, for a special microstate where many component strings share the same excitation, the emission exhibits Bose-enhancement, yielding an exponentially growing, information-carrying radiation that corresponds to the instability in gravity. This establishes a concrete gravity description of information-rich radiation for a particular non-extremal microstate and clarifies how generic microstates would yield standard Hawking-like radiation. The work strengthens the fuzzball picture by connecting gravity instabilities to quantum-statistical emission in the CFT and highlighting the role of microstate structure in black-hole radiative behavior.

Abstract

The fuzzball proposal says that the information of the black hole state is distributed throughout the interior of the horizon in a `quantum fuzz'. There are special microstates where in the dual CFT we have `many excitations in the same state'; these are described by regular classical geometries without horizons. Jejjala et.al constructed non-extremal regular geometries of this type. Cardoso et. al then found that these geometries had a classical instability. In this paper we show that the energy radiated through the unstable modes is exactly the Hawking radiation for these microstates. We do this by (i) starting with the semiclassical Hawking radiation rate (ii) using it to find the emission vertex in the CFT (iii) replacing the Boltzman distributions of the generic CFT state with the ones describing the microstate of interest (iv) observing that the emission now reproduces the classical instability. Because the CFT has `many excitations in the same state' we get the physics of a Bose-Einstein condensate rather than a thermal gas, and the usually slow Hawking emission increases, by Bose enhancement, to a classically radiated field. This system therefore provides a complete gravity description of information-carrying radiation from a special microstate of the nonextremal hole.

Figures (4)

• Figure 1: (a) A subset of $k$ strands of the component strings near a point $y$ on the $S^1$ (b) A twist operator $\sigma_k$ inserted at $y$ changes the way these stands are linked; each strand joins the next one, in a cyclical fashion (c) The vertex operator for scalar emission also creates left and right moving excitations at the location $y$.
• Figure 2: (a) Three component strings, carrying their fermionic excitation (b) The emission vertex changes these to one twisted component string. The fermions now live on fractional energy levels on this longer component string, and a pair of bosons is created as well. Angular momentum is lost because we have the 'base spin' of only one component string as opposed to three component strings; the scalar escapes with this angular momentum and the energy difference between the initial and final CFT states.
• Figure 3: (a) Traditional picture of the extremal hole (b) Geometry of a special microstate; all CFT component strings (shown in the lower diagram) are are in the same state, and this makes the geometry classical (c) A generic microstate; the CFT component strings are have a distributions of lengths and spins.
• Figure 4: (a) Traditional picture of the non-extremal hole; Hawking radiation emerges from the horizon where there is no information of the black hole state (b) Radiation from the microstates of ross; the non-extremal energy is emitted through a classical instability. The CFT state has all component strings in the same excited state, and Bose enhancement leads to a classical radiation rate (c) Our expectation for the generic non-extremal microstate. The CFT component strings have a distribution of lengths, spins and excitations, and thermal looking radiation emerges slowly. In the gravity description the complicated 'cap' region leaks the non-extremal energy slowly as information-carrying Hawking radiation.