Showing papers on "Black hole information paradox published in 1996"

Hawking radiation and unitary evolution

Abstract: We find a family of exact solutions to the semi-classical equations (including back-reaction) of two-dimensional dilaton gravity, describing infalling null matter that becomes outgoing and returns to infinity without forming a black hole. When a black hole almost forms, the radiation reaching infinity in advance of the original outgoing null matter has the properties of Hawking radiation. The radiation reaching infinity after the null matter consists of a brief burst of negative energy that preserves unitarity and transfers information faster than the theoretical bound for positive energy.

Decoherence of black holes by Hawking radiation

Abstract: We discuss in detail the semiclassical approximation for the CGHS model of two-dimensional dilatonic black holes. This is achieved by a formal expansion of the full Wheeler-DeWitt equation and the momentum constraint in powers of the gravitational constant. In highest order, the classical CGHS solution is recovered. The next order yields a functional Schr\"odinger equation for quantum fields propagating on this background. We show explicitly how the Hawking radiation is recovered from this equation. Although described by a pure quantum state, the expectation value of the number operator exhibits a Planckian distribution with respect to the Hawking temperature. We then show how this Hawking radiation can lead to the decoherence of black hole superpositions. The cases of a superposition of a black hole with a white hole, as well as of a black hole with no hole, are treated explicitly. \textcopyright{} 1996 The American Physical Society.

Hawking radiation entropy and horizon divergences

Abstract: We review the problem of divergences in one--loop thermodynamical quantities for matter fields in thermal equilibrium on a black hole background We discuss a number of results obtained for various thermodynamical quantities Then we discuss the ansatz called ``literal interpretation" of zeroth law of black hole mechanics and try to explain the diseases of the conical defect procedure in light of this ansatz Finally, an analysis of the consequences implied by our ansatz on the calculation of the partition function is made

Correlation Dynamics of Quantum Fields and Black Hole Information Paradox

Abstract: 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-equilibrium processes in the early universe and black holes, such as particle creation, entropy generation, galaxy formation, Hawking radiation, gravitational collapse, backreaction and the black hole end-state and information lost issues. Here we give a summary of the theory of correlation dynamics of quantum fields and describe how this conceptual scheme coupled with scaling behavior near the infrared limit can shed light on the black hole information paradox.

Entropy of a dressed black hole and properties of the Hartle - Hawking state

Abstract: The entropy of quantum radiation in equilibrium with a black hole is obtained in a one-loop approximation without recourse to the general first law. The approach developed does not need information about quantum corrections to the Hawking temperature and metric. It follows from properties of the Hartle - Hawking state that is finite, which confirms the universality of the Bekenstein - Hawking entropy.

A possible solution of the black hole information paradox through quantum gravity unified with other interactions

Abstract: I try to argue that the only way out of the black hole information paradox is through a unified quantum field theory of gravity and other interactions. Superstring theory is especially interesting, since in a special limit, the classical picture of 't Hooft emerges.

Quantum information and information loss in general relativity

Abstract: When it comes to performing thought experiments with black holes, Einstein-Bohr like discussions have to be re-opened. For instance one can ask what happens to the quantum state of a black hole when the wave function of a single ingoing particle is replaced by an other one that is orthogonal to the first, while keeping the total energy and momentum unaffected. Observers at $t ightarrowinfty$ will not notice any difference, or so it seems in certain calculational schemes. If one argues that this cannot be correct for the complete theory because a black hole should behave in accordance with conventional quantum mechanics, implying a unitary evolution, one is forced to believe that local quantum field theory near the black hole horizon is very different from what had hitherto been accepted. This would give us very valuable information concerning physics in the Planck length region, notably a mathematical structure very close to that of super string theory, but it does lead to conceptual difficulties. An approach that is somewhat related to this is to suspect a breakdown of General Relativity for quantum mechanical systems. It is to some extent unavoidable that Hilbert space is not invariant under general coordinate transformations because such transformations add and remove some states. Finally the cosmological constant problem also suggests that flat space-time has some special significance in a quantum theory. We suggest that a new causality principle could lead to further clues on how to handle this problem.

Quantum Fluctuations of Black Hole Geometry

Abstract: By using the minisuperspace model for the interior metric of static black holes, we solve the Wheeler·DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and th,e expansions of null rays as quantum operators. Then, the exact wave function is found as a mass eigenstate, and the radius of the apparent horizon is quantum·mechanically defined. In the evolution of the metric variables, the wave function changes from a WKB solution giving the classical trajectories to a tunneling solution. By virtue of the quantum fluctuations of the metric evolution beyond the WKB approximation, we can observe a static black hole state with the apparent horizon separating from the event horizon. Since the discovery of the Hawking radiation, much work has been devoted to the analysis of the quantum evaporation of black holes. In particular, the problem of final fates of evaporating black holes has been much debated. In Hawking'S semi­ classical calculation, the emitted radiation was found to be exactly thermal. Then, if a black hole evaporates completely, an initially pure quantum state must evolve to a mixed state. This is known as the information loss paradox. As was emphasized by Preskill, I) it is very difficult to resolve the serious puzzle in quantum mechanics and general relativity. Before reaching the final resolution, we must develop quantum theories of the black hole geometry. A possible way of treating the horizon as a quantum system is to apply the Wheeler-DeWitt equation to spherically symmetric spacetimes. In the superspace canonical formulation, the Hamiltonian and momentum constraints work as quantum equations for the physical state IJf which is a functional of the metric variables. To make the calculation tractable, Rodrigues et al. 2 ) proposed a black hole minisuper­ space model and derived the simplified Hamiltonian constraint. Unfortunately their model was found to be incompatible with the momentum constraint. 3 ) The compati­ bility between the two constraints can be recovered if we consider a local minisuper­ space model valid near the apparent horizon. 4 ) From the wave function dependent on the local metric near the apparent horizon, we can derive the mass-loss rate due to the back-reaction of Hawking radiation and show the breakdown of the semi-classical result at the final stage of complete evaporation. The Wheeler-DeWitt approach will be viable as a quantum theory of the horizon. To advance this prospect, in this paper, we want to clarify another quantum feature of the horizon from the Wheeler­ DeWitt equation. We will consider static states of a spherically symmetric black hole instead of its evolutionary states. In classical relativity the apparent horizon is always located just on the event horizon. The degeneracy of the two horizons can be removed owing to quantum fluctuations of the metric. This was first pointed out by Y ork 5 ) under the

Brick wall and quantum statistical entropy of black hole

Abstract: We discuss the statistical-mechanical entropy of black hole calculated according to 't Hooft. It is argued that in presence of horizon the statistical mechanics of quantum fields depends on their UV behavior. The ``brick wall'' model was shown to provide a correct description when the ``brick wall'' parameter is less than any UV cut-off.

On the black hole unitarity issue

Abstract: I discuss features required for preserving unitarity in black hole decay and concepts underlying such a perspective. Unitarity requires that correlations extend on the scale of the horizon. I show, in a toy model inspired by string theories, that such correlations can indeed arise. The model suggests that, after a time of order 4M ln M following the onset of Hawking radiation, quantum effects could maintain throughout the decay a collapsing star within a Planck distance of its Schwarzschild radius. In this way information loss would be avoided. The concept of black hole ``complementarity'', which could reconcile these macroscopic departures from classical physics with the equivalence principle, is interpreted in terms of weak values of quantum operators.