The black hole information paradox is one of the most important issues in theoretical physics. We review some recent progress using string theory in understanding the nature of black hole microstates. For all cases where these microstates have been constructed, one finds that they are horizon sized `fuzzballs'. Most computations are for extremal states, but recently one has been able to study a special family of non-extremal microstates, and see `information carrying radiation' emerge from these gravity solutions. We discuss how the fuzzball picture can resolve the information paradox. We use the nature of fuzzball states to make some conjectures on the dynamical aspects of black holes, observing that the large phase space of fuzzball solutions can make the black hole more `quantum' than assumed in traditional treatments.
We explore the viability of fuzzballs as candidate microstate geometries for the black hole, and their possible role in resolutions of the information paradox. We argue that if fuzzballs provide a description of black-hole microstates, then the typical fuzzball geometry can only differ significantly from the conventional black-hole geometry at a Planck-scale-distance from the horizon. However, precisely in this region, quantum fluctuations in the fuzzball geometry become large and the fuzzball geometry becomes unreliable. We verify these expectations through a detailed calculation of quantum e…
The black hole information paradox is resolved in string theory by a radical change in the picture of the hole: black hole microstates are horizon sized quantum gravity objects called `fuzzballs' instead of vacuum regions with a central singularity. The requirement of causality implies that the quantum gravity wavefunctional $Ψ$ has an important component not present in the semiclassical picture: virtual fuzzballs. The large mass $M$ of the fuzzballs would suppress their virtual fluctuations, but this suppression is compensated by the large number -- $Exp[S_{bek}(M)]$ -- of possible fuzzballs.…
The black-hole information paradox provides one of the sharpest foci for the conflict between quantum mechanics and general relativity and has become the proving-ground of would-be theories of quantum gravity. String theory has made significant progress in resolving this paradox, and has led to the fuzzball and microstate geometry programs. The core principle of these programs is that horizons and singularities only arise if one tries to describe gravity using a theory that has too few degrees of freedom to resolve the physics. String theory has sufficiently many degrees of freedom and this na…
String theory suggests that black hole microstates are quantum, horizon sized `fuzzballs', rather than smooth geometries with horizon. Radiation from fuzzballs can carry information and does not lead to information loss. But if we let a shell of matter collapse then it creates a horizon, and it seems that subsequent radiation will lead to information loss. We argue that the resolution to this problem is that the shell can tunnel to the fuzzball configurations. The amplitude for tunneling is small because we are relating two macroscopically different configurations, but the number of states tha…
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 inside its own horizon; it is therefore unable to send its information back to infinity if we disallow propagation outside the light cone. We show how the causality paradox is resolved in the fuzzball paradigm. One needs to distinguish between two kinds of Rindler spaces: (a) Rindler space obtained by choosing accelerating coordinates in Minkowski space and (…
The fuzzball construction resolves the black hole information paradox by making spacetime end just before the horizon is reached. But if there is no traditional horizon, then do we lose the elegant relations of black hole thermodynamics? Using an argument similar to modular invariance, we argue that the answer is no; the completeness of fuzzball states implies that the generic fuzzball indeed reproduces the thermal properties attributed to the traditional hole.
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 alternative…
The black-hole information paradox provides a stringent test of would-be theories of quantum gravity. String theory has made significant progress toward a resolution of this paradox, and has led to the fuzzball and microstate geometry programs. The central thesis of these programs is that only string theory has sufficiently many degrees of freedom to resolve black-hole microstructure, and that horizons and singularities are artifacts of attempting to describe gravity using a theory that has too few degrees of freedom to resolve the physics. Fuzzballs and microstate geometries recast black hole…
We study the physical properties of four-dimensional, string-theoretical, horizonless "fuzzball" geometries by imaging their shadows. Their microstructure traps light rays straying near the would-be horizon on long-lived, highly redshifted chaotic orbits. In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a black hole, while avoiding the paradoxes associated with an event horizon. Observations of the shadow size and residual glow can potentially discriminate between fuzzballs away from the scaling limit and alternative models of black compact objects.
In the fuzzball paradigm the information paradox is resolved because the black hole is replaced by an object with no horizon. One may therefore ask if observations can distinguish a traditional hole from a fuzzball. We find: (a) It is very difficult to reflect quanta off the surface of a fuzzball, mainly because geodesics starting near the horizon radius cannot escape to infinity unless their starting direction is very close to radial. (b) If infalling particles interact with the emerging radiation before they are engulfed by the horizon, then we say that we have a `firewall behavior'. We cons…
The black hole information paradox tells us something important about the way quantum mechanics and gravity fit together. In these lectures I try to give a pedagogical review of the essential physics leading to the paradox, using mostly pictures. Hawking's argument is recast as a `theorem': if quantum gravity effects are confined to within a given length scale and the vacuum is assumed to be unique, then there will be information loss. We conclude with a brief summary of how quantum effects in string theory violate the first condition and make the interior of the hole a `fuzzball'.
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 wavefunction of a collapsing shell spreads relatively quickly over this large phase space of states, invalidating the classical black hole geometry the shell would have created. We argue that a related effect may occur in the early Universe. When matter is crushed to high densities we can access a similarly large phase space of gravitational `fuzzball' solutions. W…
The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subaddditivity has sorted out the possible resolutions into three sharp categories: (A) No new physics at $r\gg l_p$; this necessarily implies remnants/information loss. A realization of remnants is given by a baby Universe attached near $r\sim 0$. (B) Violation of the `no-hair' theorem by nontrivial effects at the horizon $r\sim M$. This possibility is realized by fuzzballs in string theory, and gives unitary evaporation. (C) Having the vacuum at the horizon, …
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 small corrections theorem' to show that such an effective horizon behavior is not compatible with the requirement that the black hole radiate like a piece of coal as seen from outside. This theorem thus concretizes the fact that the proposals within the wormhole paradigm require some nonlocality linking the hole and its distant radiation. We try to illustrat…
There still exist many confusions about the black hole information paradox and its resolution. We first give a precise formulation of the paradox, in four steps A-D. Then we examine several proposals for resolving the paradox. We note that in each case one of these four steps has been ignored, so that the proposal does not really target the essence of the paradox. Finally, we give a brief summary of the fuzzball construction and argue that it resolves the paradox in string theory. This resolution contains a deep lesson -- the phase space of quantum gravity is so large that the measure in the p…
The idea of holography in gravity arose from the fact that the entropy of black holes is given by their surface area. The holography encountered in gauge/gravity duality has no such relation however; the boundary surface can be placed at an arbitrary location in AdS space and its area does not give the entropy of the bulk. The essential issues are also different between the two cases: in black holes we get Hawking radiation from the `holographic surface' which leads to the information issue, while in gauge/gravity duality there is no such radiation from the boundary surface. To resolve the inf…
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 radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a `theorem': assuming `traditional' physics at the horizon and usual assumptions of locality we will be forced into m…
A concise survey of the black hole information paradox and its current status is given. A summary is also given of recent arguments against remnants. The assumptions underlying remnants, namely unitarity and causality, would imply that Reissner Nordstrom black holes have infinite internal states. These can be argued to lead to an unacceptable infinite production rate of such black holes in background fields. (To appear in the proceedings of the PASCOS symposium/Johns Hopkins Workshop, Baltimore, MD, March 22-25, 1995).
When a shell collapses through its horizon, semiclassical physics suggests that information cannot escape from this horizon. One might hope that nonperturbative quantum gravity effects will change this situation and avoid the `information paradox'. We note that string theory has provided a set of states over which the wavefunction of the shell can spread, and that the number of these states is large enough that such a spreading would significantly modify the classically expected evolution. In this article we perform a simple estimate of the spreading time, showing that it is much shorter than …
We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a refinement of the paradox that makes essential reference to the black-hole interior. This analysis leads to a broadly-applicable physical principle: in a theory of quantum gravity, a copy of all the information on a Cauchy slice is also available near the boundary of the slice. This principle can be made precise and established -- under weak assumptions, and using …
In recent years a statistical mechanics description of particles, fields and spacetime based on the concept of quantum open systems and the influence functional formalism has been introduced. It reproduces in full the established theory of quantum fields in curved spacetime and contains also a microscopic description of their statistical properties, such as noise, fluctuations, decoherence, and dissipation. This new framework allows one to explore the quantum statistical properties of spacetime at the interface between the semiclassical and quantum gravity regimes, as well as important non-equ…
This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given by the $A/4$ (where $A$ is the area of the black hole horizon), but for which the assignment of a classical entropy to t…
To understand the information loss paradox in a consistent way, we provide a brief big picture that describes both outside and inside a black hole. We summary several ideas including the Euclidean path integral, the entanglement entropy, and the quantum gravitational treatment for the singularity. This integrated discussion can provide an alternative point of view toward the ultimate resolution of the information loss paradox.
It has been argued that small corrections to evolution arising from non-geometric effects can resolve the information paradox. We can get such effects, for example, from subleading saddle points in the Euclidean path integral. But an inequality derived in 2009 using strong sub-additivity showed that such corrections {\it cannot} solve the problem. As a result we sharpen the original Hawking puzzle: we must either have (A) new (nonlocal) physics or (B) construct hair at the horizon. We get correspondingly different approaches to resolving the AMPS puzzle. Traditional complementarity assumes (A)…
We consider three fundamental issues in quantum gravity: (a) the black hole information paradox (b) the unboundedness of entropy that can be stored inside a black hole horizon (c) the relation between the black hole horizon and the cosmological horizon. With help from the small corrections theorem, we convert each of these issues into a sharp conflict. We then argue that all three conflicts can be resolved by the following hypothesis: {\it the vacuum wavefunctional of quantum gravity contains a `vecro' component made of virtual fluctuations of configurations of the same type that arise in the …
Two seemingly distinct notions regarding black holes have captured the imagination of theoretical physicists over the past decade: First, black holes are conjectured to be fast scramblers of information, a notion that is further supported through connections to quantum chaos and decay of mutual information via AdS/CFT holography. Second, black hole information paradox has motivated exotic quantum structure near horizons of black holes (e.g., gravastars, fuzzballs, or firewalls) that may manifest themselves through delayed gravitational wave echoes in the aftermath of black hole formation or me…
The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity do not exhibit any such breakdown, and this forces us into a difficult corner: either we must give up quantum mechanics or we must accept the existence of troublesome `remnants'. In string theory, however, the fundamental quanta are extended objects, and it turns out that the bound states of such objects acquire a size that grows with the number of quanta i…
We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semi-classical solution to the cosmological constant problem(s), and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. …
In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem, or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. It was recently pointed out that such near-horizon structures can lead to late-time echoes in the black hole merger gravitational wave signals that are otherwise indistinguishable from GR. We search for…
These are lecture notes for the 1992 Erice Workshop on Theoretical Physics. They first present a summary of the paradox of information loss to black holes, of its proposed resolutions, and of the flaws in the proposed resolutions. There follows a review of recent attempts to attack this problem, and other issues in black hole physics, using two-dimensional dilaton gravity theories as toy models. These toy models contain collapsing black holes and have for the first time enabled an explicit semiclassical treatment of the backreaction of the Hawking radiation on the geometry of an evaporating bl…
A generic feature of nearly out-of-equilibrium dissipative systems is that they resonate through a set of quasinormal modes. Black holes - the absorbing objects par excellence - are no exception. When formed in a merger, black holes vibrate in a process called "ringdown", which leaves the gravitational-wave footprint of the event horizon. In some models of quantum gravity which attempt to solve the information-loss paradox and the singularities of General Relativity, black holes are replaced by regular, horizonless objects with a tiny effective reflectivity. Motivated by these scenarios, here …
