Related papers: Modave Lectures on Horizon-Size Microstructure, Fu…

Quite recently, some new mathematical approaches to black holes have appeared in the literature. They do not rely on the classical concept of event horizon -- which is very global, but on the local concept of hypersurfaces foliated by…

The black hole information paradox is really a combination of two problems: the causality paradox and the entanglement problem. The causality paradox arises because in the semiclassical approximation infalling matter gets causally trapped…

In recent years we have come to understand how the information paradox is resolved in string theory. The huge entropy $S_{bek}={A\over 4G}$ of black holes is realized by an explicit set of horizon sized `fuzzball' wavefunctions. The…

One can obtain very large classes of horizonless microstate geometries corresponding to near-extremal black holes by placing probe supertubes whose action has metastable minima inside certain supersymmetric bubbling solutions. We show that…

The black hole paradigm, while remarkably successful, raises fundamental questions-both classical and quantum-about the nature of spacetime, horizons, and singularities. Black hole mimickers, horizonless ultra-compact objects, have emerged…

The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the…

Microstate geometries are proposed microstates of black holes which can be described within supergravity. Even though their number may not reproduce the full entropy of black holes with finite-sized horizons, they still offer a glimpse into…

We examine an interesting set of recent proposals describing a `wormhole paradigm' for black holes. These proposals require that in some effective variables, semiclassical low-energy dynamics emerges at the horizon. We prove the `effective…

Black holes are the hydrogen atoms of quantum gravity. For instance solving the information loss paradox will likely require a deep understanding of how the long-sought quantum gravity theory works. In this thesis we explore how black holes…

We give an elementary review of black holes in string theory. We discuss BPS holes, the microscopic computation of entropy and the `fuzzball' picture of the black hole interior suggested by microstates of the 2-charge system.

Assume that there exists a fundamental theory of gravity which has a fundamental length scale and which is capable of explaining black hole evolution process fully in terms of fundamental microscopic degrees of freedom. The resultant…

Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information…

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past ten years in string theory, brane-world models and quantum gravity. Through the famous…

We examine the stability of the nonextremal D1-D5-P black hole solutions. In particular, we look for the appearance of a superradiant instability for the spinning black holes but we find no evidence of such an instability. We compare this…

The aim of these lectures is to give an introduction to several topics which lie at the intersection of string theory, gravity theory and gravity phenomenology. One successively reviews: (i) the "membrane" approach to the dissipative…

In these notes we discuss the topological nature of some problems in condensed matter physics. We adopt the language of differential geometry to present this subject and our aim is to develop some intuition towards concepts like curvature,…

For extremal black holes the fuzzball conjecture says that the throat of the geometry ends in a quantum `fuzz', instead of being infinite in length with a horizon at the end. For the D1-D5 system we consider a family of sub-ensembles of…

Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest…

This lecture reviews the black hole information paradox and briefly appraises some proposed resolutions in view of developments in string theory. It goes on to give an elementary introduction to the holographic principle.

We study two-charge fuzzball geometries, with attention to the use of the proper duality frame. For zero angular momentum there is an onion-like structure, and the smooth D1-D5 geometries are not valid for typical states. Rather, they are…