The fuzzball proposal for black holes (0804.0552v2)

Abstract: The fuzzball proposal states that associated with a black hole of entropy S there are exp S horizon-free non-singular solutions that asymptotically look like the black hole but generically differ from the black hole up to the horizon scale. These solutions, the fuzzballs, are considered to be the black hole microstates while the original black hole represents the average description of the system. The purpose of this report is to review current evidence for the fuzzball proposal, emphasizing the use of AdS/CFT methods in developing and testing the proposal. In particular, we discuss the status of the proposal for 2 and 3 charge black holes in the D1-D5 system, presenting new derivations and streamlining the discussion of their properties. Results to date support the fuzzball proposal but further progress is likely to require going beyond the supergravity approximation and sharpening the definition of a "stringy fuzzball". We outline how the fuzzball proposal could resolve longstanding issues in black hole physics, such as Hawking radiation and information loss. Our emphasis throughout is on connecting different developments and identifying open problems and directions for future research.

• The paper demonstrates that fuzzball solutions provide horizonless, non-singular microstates that account for black hole entropy.
• It employs AdS/CFT correspondence to map black hole microstates to dual field theory states, challenging traditional event horizon concepts.
• Tests in the D1-D5 system and progress in three-charge models highlight avenues for resolving the black hole information loss paradox.

An Overview of the Fuzzball Proposal for Black Holes

The paper "The Fuzzball Proposal for Black Holes" by Kostas Skenderis and Marika Taylor provides an extensive examination of the fuzzball hypothesis, a proposition in string theory aiming to resolve persistent enigmas in black hole physics. The authors compile and critique various strands of evidence supporting this hypothesis, centering their analysis on the employment of AdS/CFT methodologies in advancing and testing the fuzzball concept. Their paper particularly explores solutions within the D1-D5 system for two and three charge black holes.

Key Insights and Methodologies

The fuzzball proposal postulates that for a black hole with entropy $S$, there exists an exponential number, $\exp(S)$, of horizon-free, non-singular solutions. These candidate solutions - the so-called fuzzballs - are not singular and resemble the black hole up to the horizon scale, diverging from the classical notion of black holes being singular with a horizon. These fuzzballs represent specific microstates that contribute to the total entropy of a black hole, while the classical black hole solution reflects an average over such states. This perspective attempts to demystify black hole entropy, traditionally linked to the horizon area via the Bekenstein-Hawking formula.

The authors utilize the tools of the AdS/CFT correspondence, a duality establishing an equivalence between a theory of gravity in Anti-de Sitter (AdS) space and a conformal field theory (CFT) without gravity. This duality facilitates the understanding of black hole microstates, by equating them to certain states within a dual field theory, and supports a unitary framework for black hole dynamics, contesting the classical black hole information paradox rooted in non-unitary evolution.

Findings and Theoretical Implications

Skenderis and Taylor argue that the fuzzball hypothesis could address foundational issues in black hole physics, including Hawking radiation and the information loss paradox. They suggest that the entropy source in fuzzball solutions emanates from the volume of the classical phase space, negating information loss as matter will eventually return to infinity without being temporarily sequestered by a horizon.

For two-charge systems, the fuzzball solutions, built upon the D1-D5 setup, can be constructed to encapsulate microstate geometries corresponding to the underlying black hole configuration. The computations of these geometric solutions have been challenged by their reliance on AdS asymptotic backgrounds, which simulate the near-horizon regions of black holes. Tests in three-charge systems using similar techniques show incremental progress, offering a portrayal of field theory states from supergravity perspectives.

Challenges and Future Directions

While the evidence compiled fortifies the fuzzball proposition, the authors articulate several areas necessitating further inquiry. Principal among these is the endeavor to derive solutions for black holes with macroscopic horizons beyond the supergravity limit, potentially involving more nuanced considerations of stringy corrections. Moreover, rendering a comprehensive framework that accommodates all microstates remains an intricate challenge, with current fuzzball solutions illuminating only a portion of the theoretical landscape.

Conceptually, the fuzzball hypothesis propounds a paradigm shift whereby black holes manifest as conglomerates of microstate geometries, devoid of traditional event horizons or singularities. Future research may enhance this prospect by refining the coupling of supergravity solutions with quantum stringy states, thereby elucidating the demarcations between quantum mechanics and classical gravity.

In sum, "The Fuzzball Proposal for Black Holes" posits a cogent narrative of black holes in string theory, seeking to reconcile them with quantum mechanics through sophisticated theoretical constructs. As the exploration of fuzzball solutions progresses, it continues to contour our comprehension of quantum gravity, rendering tangible the abstruse properties of black holes.