We consider a novel approach to address the black hole information paradox (BHIP). The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as "the measurement problem". The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as "Continuous Spontaneous Localization" (CSL), which was originally developed in the context of many particle non-relativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two dimensional Callan-Giddings-Harvey-Strominger (CGHS) model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.

The process of black hole evaporation resulting from the Hawking effect has generated an intense controversy regarding its potential conflict with quantum mechanics' unitary evolution. A recent set of works by a collaboration involving one of us, have revised the controversy with the aims of, on one hand, clarifying some conceptual issues surrounding it, and, at the same time, arguing that collapse theories have the potential to offer a satisfactory resolution of the so-called paradox. Here we show an explicit calculation supporting this claim using a simplified model of black hole creation and evaporation, known as the CGHS model, together with a dynamical reduction theory, known as CSL, and some speculative, but seemingly natural ideas about the role of quantum gravity in connection with the would-be singularity. This work represents a specific realization of general ideas first discussed in [1] and a complete and detailed analysis of a model first considered in [2].

We review the relation between AdS spacetime in 1+2 dimensions and the BTZ black hole. Later we show that a ground state in AdS spacetime becomes a thermal state in the BTZ black hole. We show that this is true in the bulk and in the boundary of AdS spacetime. The existence of this thermal state is tantamount to say that the Unruh effect exists in AdS spacetime and becomes the Hawking effect for an eternal BTZ black hole. In order to make this we use the correspondence introduced in Algebraic Holography between algebras of quasi-local observables associated to wedges and double cones regions in the bulk of AdS spacetime and its conformal boundary respectively. Also we give the real scalar quantum field as a concrete heuristic realization of this formalism. * leonardo.ortiz@uniofyorkspace.net

Abstract. We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background', QFT-based, approaches to holography) and in mainstream string-theoretic 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the point of view of QFT in curved spacetime -in the framework of 't Hooft's 'brick wall' model -with the understanding based on Maldacena AdS/CFT. We show that the brickwall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2 dimensional Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'complementarity principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.

We show that there is no superradiance in the rotating BTZ black hole for vanishing boundary conditions at infinity for the real scalar field. * leonardo.ortiz@uniofyorkspace.net

This paper considers the quantum collapse of infinitesimally thin dust shells in 2 + 1 gravity. In 2 + 1 gravity a shell is no longer a sphere, but a ring of matter. The classical equation of motion of such shells in terms of variables defined on the shell has been considered by Peleg and Steif [1], using the 2 + 1 version of the original formulation of Israel [2], and Crisóstomo and Olea [3], using canonical methods. The minisuperspace quantum problem can be reduced to that of a harmonic oscillator in terms of the curvature radius of the shell, which allows us to use wellknown methods to find the motion of coherent wave packets that give the quantum collapse of the shell. Classically, as the radius of the shell falls below a certain point, a horizon forms. In the quantum problem one can define various quantities that give "indications" of horizon formation. Without a proper definition of a "horizon" in quantum gravity, these can be nothing but indications.It is a great pleasure to be able to contribute to this special volume in honor of Octavio Obregon. One of us [M.R.] has known Octavio for more than 30 years and has collaborated with him on many fruitful projects. We both want to wish him many more productive years and continued success.

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We show that there is no superradiance for the Dirac field in the rotating BTZ black hole if the field vanishes at infinity. Then we outline the calculation of the expression for the renormalized energy-momentum tensor, the effective action as well as the heat kernel for the Dirac field for the BTZ black hole. Finally we point out how to construct the Hartle-Hawking-Israel state for the real scalar field in the non-rotating BTZ black hole in two and three dimensions.