Deformed Density Matrix and Quantum Entropy of the Black Hole

In the present work the approach - density matrix deformation - earlier developed by the author to study a quantum theory of the Early Universe (Planck's scales) is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibility for application of the proposed approach to the calculation of quantum entropy of a black hole is considered.Comment: 17 pages, Latex, new referenc

Non-Unitary and Unitary Transitions in Generalized Quantum Mechanics, New Small Parameter and Information Problem Solving

Quantum Mechanics of the Early Universe is considered as deformation of a well-known Quantum Mechanics. Similar to previous works of the author, the principal approach is based on deformation of the density matrix with concurrent development of the wave function deformation in the respective Schr{\"o}dinger picture, the associated deformation parameter being interpreted as a new small parameter. It is demonstrated that the existence of black holes in the suggested approach in the end twice causes nonunitary transitions resulting in the unitarity. In parallel this problem is considered in other terms: entropy density, Heisenberg algebra deformation terms, respective deformations of Statistical Mechanics, - all showing the identity of the basic results. From this an explicit solution for Hawking's informaion paradox has been derived.Comment: 18 page

Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity

In this work it is demonstrated that, provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The corresponding infinitesimal quantities in this case must be replaced by the "minimal variations possible" -- finite quantities dependent on the existent energies. As a result, the initial low-energy theory (quantum theory or general relativity) inevitably must be replaced by a minimal-length theory that gives very close results but operates with absolutely other mathematical apparatus.Comment: 23 pages, Late

Probable Entropic Nature of Gravity in Ultraviolet and Infrared Limits, Part I. An Ultraviolet Case

This work presents a study of the possibility for extending the well-known results of E.Verlinde concerning the entropic nature of gravity to the ultraviolet region (Planck's energies) and also the derivation of quantum corrections to Einstein EquationsComment: 20 pages, Latex, v.3, some important correction

Quantum Theory at Planck Scale, Limiting Values, Deformed Gravity and Dark Energy Problem

Within a theory of the existing fundamental length on the order of Planck's a high-energy deformation of the General Relativity for the space with horizon has been constructed. On this basis, Markov's work of the early eighties of the last century has been given a new interpretation to show that the heuristic model considered by him may be placed on a fundamental footing. The obtained results have been applied to solving of the dark energy problem, making it possible to frame the following hypothesis: a dynamic cosmological term is a measure of deviation from a thermodynamic identity (the first law of thermodynamics) of the high-energy (Planck's) deformation of Einstein equations for horizon spaces in their thermodynamic interpretation.Comment: 30 pages, Latex. arXiv admin note: substantial text overlap with arXiv:1003.4523, arXiv:0911.5597, arXiv:1006.497