Modave Lectures on Horizon-Size Microstructure, Fuzzballs and Observations

Abstract

These lecture notes discuss various aspects of the fuzzball paradigm, microstate geometries, and their role in gravitational phenomenology. We briefly introduce the information paradox and discuss how the fuzzball paradigm aims to resolve it. Then, some important families of fuzzball solutions in supergravity, called microstate geometries, are explored: multi-centered bubbling geometries and superstrata. Finally, we will review some very recent developments of the phenomenology of fuzzballs and delineate the exciting opportunities as well as the limitations of studying fuzzballs as alternatives to black holes in current and future observations. A guide to these lecture notes These notes are a brief introduction to fuzzballs, microstate geometries, and their role as compact objects in gravitational phenomenology for precision black hole observations. They are based on lectures I gave at the XVII Modave Summer School in Mathematical Physics in September 2021. These notes are emphatically not meant as an alternative to more comprehensive lecture notes, such as [1] and [2] for multi-centered bubbled geometries, or [3] for superstrata. Rather, if [1, 2, 3] are the “manual” for these geometries, then these notes should be seen as the “Quick start guide”: a practical collection of some of the most pertinent material that one needs to understand and start working with these geometries. (Note that, despite the length of this entire document, the main part — Section 1 introducing fuzzballs and Section 2 discussing multi-centered geometries — is under 20 pages.) It is also not necessary to go through these entire notes, or even to go through each section sequentially; the reader can pick and choose the topics which they are interested in learning about. These notes are also complementary to my review [4] on “Fuzzballs & Observations”, which is an overview of fuzzball phenomenology, meant to introduce the relevant concepts and ideas (both in fuzzballs and in phenomenology) without too many technical details of the geometries. By contrast, these notes give precisely the minimal technical details necessary to actually start performing concrete calculations with microstate geometries. 1 ar X iv :2 20 2. 11 39 4v 1 [ he pth ] 2 3 Fe b 20 22 Section 1 introduces the fuzzball paradigm, discussing mechanisms and concepts that lie at the basis of the existence of microstructure. The multi-centered bubbling geometries are derived and discussed in Section 2. Superstrata are discussed in Section 3, albeit with quite a bit less detail. Section 4 discusses applying fuzzballs and horizon-scale microstructure to observations and gravitational phenomenology. The appendices collect some additional information. Appendix A is a brief overview of some concepts in string theory that arise frequently in the discussion of fuzzballs. Appendix B is a reference containing all the necessary information to construct multicentered solutions (from Section 2). Appendix C is a collection of six exercises (including solutions), most on multi-centered geometries and some of their more important properties.