Time dependent Schrödinger equation for black hole evaporation: No information loss

Abstract

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state"1 . This was the starting point of the popular "black hole (BH) information paradox".In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semiclassical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schröedinger equations can be 1 Verbatim from ref. 2 1 used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution.In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.To the memory of the latter IFM Secretary Franco Pettini.

Initiating the Effective Unification of Black Hole Horizon Area and Entropy Quantization with Quasi-Normal Modes

“…Subsequently, we identified a series of damped harmonic oscillator QNM configurations and strictly thermal corrections that were systematically deployed to encode a BH's behavior and quantization of area and entropy. Next, we shifted to the strictly thermal spectrum deviation corrections [16] that inspired numerous crucial follow-up explorations [4,34,35,[37][38][39][40] with a subsequent application of QNMs and effective states [31,32,[42][43][44].…”

“…For this, we chronologically reviewed a series of imperative corrections that eventually permits the Hawking radiation and the Bekenstein-Hawking horizon area and entropy spectrum to be generalized from strictly thermal to nonstrictly thermal with QNMs and effective states [31,32,[42][43][44], which are significant because they further exemplify the underlying QG theory. In general, all of the works presented in this review are important to physics because the characteristic physical laws of BHs must be understood in order to resolve, for example, the puzzles imposed by the BH information paradox and firewalls [1][2][3][4][5] in nature. Henceforth, the convergence of such outcomes has launched an effective unification that begins to merge, generalize, and simplify an array of strictly thermal and nonstrictly thermal quantization approaches to a single, consolidated approach of effective states that acknowledges further insight into the physical structure, behavior, and effects of BHs.…”

“…In general, the laws of classical and modern physics break down when attempts are made to rigorously characterize the behavior of BHs and their effects. In order to advance science, fundamental problems such as the BH information paradox and event horizon firewalls [1][2][3][4] must be understood and nullified so the physical laws can be "upgraded" via the scientific method and tested in laboratory experiments [5].…”

On Quasi-Normal Modes, Area Quantization and Bohr Correspondence Principle

“…This is surely consistent with the unitarity of the underlying quantum gravity theory and with the idea that information should come out in BH evaporation. We have indeed recently shown that the time evolution of the Bohr-like BH obeys a time dependent Schrödinger equation [26]. In that way, the physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix [26].…”

“…We have indeed recently shown that the time evolution of the Bohr-like BH obeys a time dependent Schrödinger equation [26]. In that way, the physical state and the correspondent wave function are written in terms of an unitary evolution matrix instead of a density matrix [26]. Thus, the final state results to be a pure quantum state instead of a mixed one while the entanglement problem connected with the information paradox is solved showing that the emitted radiation is entangled with BH QNMs [26].…”