Modave Lectures on Fuzzballs and Emission from the D1-D5 System

TL;DR

The notes address the black hole information paradox by juxtaposing the fuzzball proposal with detailed gravity and D1-D5 CFT analyses. Using D1-D5-P geometries, they show that Hawking radiation, superradiance, and ergoregion emission are unified manifestations of the same underlying process in the CFT, whether the gravity description includes a horizon or a smooth cap. The work provides explicit gravity calculations of absorption/emission, greybody factors, and spectral flows, alongside CFT amplitudes and spectral flow relations, to argue that typical fuzzball microstates reproduce black hole thermodynamics while maintaining unitarity. The findings reinforce a paradigm in which black holes are effective coarse-grained descriptions of ensembles of horizon-scale microstates, with radiation carrying information through microstate structure. This has broad implications for quantum gravity, holography, and the microscopic understanding of black hole entropy and dynamics.

Abstract

These lecture notes present an introduction to the fuzzball proposal and emission from the D1-D5 system which is geared to an audience of graduate students and others with little background in the subject. The presentation begins with a discussion of the Penrose process and Hawking radiation. The fuzzball proposal is then introduced, and the two- and three-charge systems are reviewed. In the three-charge case details are not discussed. A detailed discussion of emission calculations for D1-D5-P black holes and for certain non-extremal fuzzballs from both the gravity and CFT perspectives is included. We explicitly demonstrate how seemingly different emission processes in gravity, namely, Hawking radiation and superradiance from D1-D5-P black holes, and ergoregion emission from certain non-extremal fuzzballs, are only different manifestations of the same phenomenon in the CFT.

Figures (11)

• Figure 1: The Penrose process. In (a) a particle of energy $E_0>0$ is sent into the ergoregion. In (b) the particle splits into two particles; one with energy $E_1 > E_0$ escaping out, and the other with energy $E_2<0$ falling into the horizon.
• Figure 2: A Penrose diagram of a spherically symmetric spacetime in which gravitational collapse to a Schwarzschild black hole takes place. Outgoing waves starting from $\mathcal{J}^+$ propagated backwards end up on $\mathcal{J}^-$.
• Figure 3: Cartoons for (a) fuzzball and (b) fuzzring solutions for two profile functions each. The green (shaded) region is the region in which the typical solutions differ very much from each other. The metric for typical states is similar outside the green (shaded) region. If one puts a stretched horizon on the green (shaded) region one gets a coarse grained entropy that goes like $S_{\mathrm{stretched}} \sim \sqrt{n_1 n_5}$ for the fuzzballs and like $S_{\mathrm{stretched}} \sim \sqrt{n_1 n_5 - J}$ for the fuzzrings.
• Figure 4: (a): The geometry of a black hole has an outer flat space connected by a neck to a throat which ends in a horizon with a singularity hidden behind. (b) The geometry of a generic state has outer flat space connected by a neck to a throat which ends in a smooth cap without horizons and singularities.
• Figure 5: (a) The geometry of black hole is flat at infinity, then there is a 'neck' region, and further-in the geometry takes the form of $AdS_{3}\times S^3$. The $AdS_{3}\times S^3$ region is a part of the BTZ black hole. (b) The geometry of fuzzballs is also flat at infinity followed by a 'neck' region. Still further in, the geometry ends in a 'fuzzball cap' whose structure is determined by the choice of microstate. For the states found in Jejjala:2005yu the cap and the AdS region is simply the global AdS.