Global Structure of Five-dimensional BPS Fuzzballs (1305.0957v1)

Abstract: We describe and study families of BPS microstate geometries, namely, smooth, horizonless asymptotically-flat solutions to supergravity. We examine these solutions from the perspective of earlier attempts to find solitonic solutions in gravity and show how the microstate geometries circumvent the earlier "No-Go" theorems. In particular, we re-analyse the Smarr formula and show how it must be modified in the presence of non-trivial second homology. This, combined with the supergravity Chern-Simons terms, allows the existence of rich classes of BPS, globally hyperbolic, asymptotically flat, microstate geometries whose spatial topology is the connected sum of N copies of S^2 x S^2 with a "point at infinity" removed. These solutions also exhibit "evanescent ergo-regions," that is, the non-space-like Killing vector guaranteed by supersymmetry is time-like everywhere except on time-like hypersurfaces (ergo-surfaces) where the Killing vector becomes null. As a by-product of our work, we are able to resolve the puzzle of why some regular soliton solutions violate the BPS bound: their spactimes do not admit a spin structure.

Overview of the Global Structure of Five-dimensional BPS Fuzzballs

The paper "Global Structure of Five-dimensional BPS Fuzzballs" by G.W. Gibbons and N.P. Warner explores the intricate geometry of BPS microstate geometries, often referred to as fuzzballs, in the framework of five-dimensional supergravity. These solutions aim to resolve paradoxes related to the quantum theory of black holes by providing a geometric representation of black-hole microstates without event horizons or singularities.

Key Insights

The authors critically evaluate past methods for identifying solitonic solutions in gravity, especially those that have been encumbered by various "No-Go" theorems. The fuzzball solutions circumvent these theorems by leveraging second homology and Chern-Simons terms inherent in supergravity models. This breakthrough is a significant step forward, as it enables the construction of a wide variety of BPS geometries with intricate topologies.

Numerical Results and Bold Claims

One of the numerical highlights of the paper lies in the modification of the Smarr formula, incorporating contributions from non-trivial second homology and Chern-Simons interactions. The existence of BPS fuzzballs, which appear as stable, horizonless spacetimes, challenges the conventional belief encapsulated by "no solitons without horizons." Moreover, these solutions exhibit complex spatial topology described by connected sums of multiple $S^2 \times S^2$, providing evidence that the proposed mathematical framework effectively accommodates non-trivial topological transformations.

Theoretical Implications

The theoretical implications of this research are profound. By demonstrating viable candidates for black-hole microstates using fuzzballs, this work not only contributes to the ongoing discourse surrounding the information paradox but also provides new pathways for constructing stable solutions in higher-dimensional theories. This indicates potential extensions and modifications considering quantum geometry and deeper understanding of supersymmetry in string theory.

Practical Implications and Future Directions

Practically, these findings suggest the possibility of identifying stable stellar remnants, or topological stars, maintained by topological interactions rather than event horizons. Fuzzballs could play a critical role in understanding astrophysical phenomena within a semi-classical regime when explored deeply within string-theoretical frameworks. For future research, one of the intriguing directions includes translating BPS fuzzball characteristics into non-BPS regimes, identifying broader applications in cosmic structures, and exploring more comprehensive supersymmetric models.

Conclusion

In summary, this paper advances the theoretical understanding of fuzzballs, addressing key limitations from preceding solutions while opening new avenues for the paper of quantum gravity. The work done by Gibbons and Warner provides a crucial foundation for further exploration in the domain of supergravity and string theory, potentially leading to revolutionary developments in black hole physics.