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I will classify the options to solve the black hole information loss problem by how radical a departure from semi-classical gravity they require outside the quantum gravitational regime. I will argue that the most plausible and conservative conclusion is that the problem of information loss originates in the presence of the singularity and that thus effort should be focused on understanding its avoidance. A consequence of accepting the accuracy of the semi-classical approximation is the surface interpretation of black hole entropy. I will summarize the arguments that have been raised for and against such scenarios. Reference: http://arxiv.org/abs/0901.3156

String theory gives a consistent theory of quantum gravity, so we can ask about the nature of black hole microstates in this theory. Studies of extremal and near-extremal microstates indicate that these microstates do not have a traditional horizon, which would have no data about the microstate in its vicinity. Instead, the information of the microstate is distributed throughout a horizon sized quantum `fuzzball'. If this picture holds for all microstates then it would resolve the information paradox. We review recent progress in the area, including some results on non-extremal states. We also discuss some conjectures about black hole dynamics suggested by the structure of fuzzballs.

Theories which have fundamental information destruction or decoherence are motivated by the black hole information paradox. However they have either violated conservation laws, or are highly non-local. Here, we show that the tension between conservation laws and locality can be circumvented by constructing a relational theory of information destruction. In terms of conservation laws, we derive a generalization of Noether's theorem for general theories, and show that symmetries imply a restriction on the type of evolution permissible. With respect to locality, we distinguish violations of causality from the creation or destruction of separated correlations. We show that violations of causality need not occur in a relational framework -- the only non-locality is that correlations decay faster than one might otherwise expect or can be created over spatial distances. The theories can be made time-symmetric, thus imposing no arrow of time.

Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. Two properties follow from this purely gravitational behavior. The first, 'Boundary Unitarity,' holds under AdS-like boundary conditions. This is the statement that the algebra of boundary observables is independent of time; i.e., that the algebra of boundary observables at any one time t_1 in fact coincides with the algebra of boundary observables at any other time t_2. As a result, any information available at the boundary at time t_1 remains available at any other time t_2. The second, 'Perturbative Holography,' holds under either AdS-like or asymptotically flat boundary conditions. In the AdS context, it is the statement that the algebra of boundary observables at any time t includes all perturbative observables anywhere in the spacetime. In the asymptotically flat context, Perturbative Holography is that statement that the algebra of observables on I^+ within any neighborhood of i^0 contains all perturbative observables. Perturbative Holography holds about any classical solution with a regular past infinity; i.e., spacetimes which collapse to form classical black holes are explicitly allowed. We derive the above properties and discuss their implications for information in black hole evaporation.

In this talk we introduce loop quantum gravity and we apply the theory to the black hole singularity problem. The Schwarzschild black hole solution inside the event horizon coincides with the Kantowski-Sachs space-time and we can study a simple spherically symmetric mini-superspace model. We show the classical black hole singularity is controlled by the quantum theory and the space-time can be dynamically extended beyond the classical singularity. We consider a semiclassical analysis of the black hole in LQG and we focus our attention on the space-time structure. The semiclassical solution is regular everywhere and similar to the Reissner-Nordstrom metric. The LQG black hole metric interpolates between two asymptotically flat regions, the 'r=infinity' region and the 'r=0' region. The metric is self-dual in the sense it is invariant under the symmetry (r ->1/r) which relates small and large distances. We study the thermodynamics of the semiclassical solution.

I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon 'degrees of freedom''; is finite because the deep structure of spacetime is discrete; is ``objective'' thanks to the distinguished coarse graining provided by the horizon; and obeys the second law of thermodynamics precisely because the effective dynamics of the exterior region is not unitary.

In this talk I will describe a topos formulation of consistent histories obtained using the topos reformulation of standard quantum mechanics put forward by Doering and Isham. Such a reformulation leads to a novel type of logic with which to represent propositions. In the first part of the talk I will introduce the topos reformulation of quantum mechanics. I will then explain how such a reformulation can be extended so as to include temporally-ordered collection of propositions as opposed to single time propositions. Finally I will show how such an extension will lead to the possibility of assigning truth values to temporal propositions.

The handling of the constraints on initial data is a major issue in most canonical formulations of general relativity. Since the 1960s unconstrained initial data for GR that living on null hypersurfaces has been known, but no canoncial formulation based on these data was developed due to conceptual and technical difficulties. I will explain how these dificulties have been overcome and outline the resulting canonical framework. I will also explain how this might be the ideal setting to attempt a proof of the Bousso entropy bound, or to incorporate the associated holographic principle in a quantization of gravity.

New spin foam models for gravity have been recently proposed to deal with the shortcomings of the Barrett-Crane model. In particular, they draw a closer connection between the Loop Quantum Gravity and the Spin Foam approaches to non perturbative quantum gravity. In this talk, I will present the construction for the case of Lorentzian signature and finite Immirzi parameter. An area operator can be defined and its spectrum agrees with the one defined in LQG. Finally, the amplitude is shown to be finite after a suitable regularization.

We give an overview of what we have called the \'LQG spinfoam models,\' that provide a spinfoam dynamics for LQG, for arbitrary values of the Barbero-Immirzi parameter in both Lorentzian and Euclidean signatures. The key motivation behind these models was to modify the Barrett-Crane model, by handling more carefully certain constraints, called simplicity constraints, which become second class in the quantum theory. As a result, the kinematics of the models exactly match those of LQG. The goal of this talk is to provide a broad picture of the significance of these models and their basic ideas.

I will review the present status of the black hole entropy computation in Loop Quantum Gravity within the isolated horizon framework. Starting from the recently discovered discretization effect, I will give an overview of the subsequent developments that have been obtained motivated by it. Through this further analysis of the problem I will present some new related results and the promising new open windows that they give rise to.

While analogue models for gravity have so far provided some insights on the kinematical aspects of general relativity, the emergence of gravitational dynamics is still unclear. In this talk I will present two models which aim at filling this gap. In the first one a BEC model is considered, to uncover the gravitational dynamics hidden in these systems. In particular, the emergence of a modified Newtonian dynamics and of the cosmological constant will be discussed. A second model will be used to show how Nordstrom theory of gravity emerges from a system defined in Minkowski spacetime, showing how background independent theories of gravity could emerge from background dependent models.