Abstract
The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schrödinger’s type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states in this model.
Highlights
Since the discovery that black holes would have to emit radiation, there have been proposals to explain the loss of information associated with the apparent conversion of pure to mixed quantum states
It has been emphasised over the time the role of the gravitational back reaction effect [13,14] of Hawking radiation on the event horizon as a way to allow the information accumulated within the black hole to be encoded in the outgoing radiation
The emergence of a mechanism in which all the black hole information would be accessible at the event horizon, is somehow similar to what happens with a hologram [15]
Summary
Since the discovery that black holes would have to emit radiation, there have been proposals to explain the loss of information associated with the apparent conversion of pure to mixed quantum states. It is important to notice that, even though, a full study of the time evolution of the Hawking radiation and black hole quantum states was performed when a simple back reaction term is introduced, an important part of the discussion about the time evolution of the resulting entangled state was left incomplete It is exactly the motivation of this paper to address the problem of explicitly describe the time evolution of the degree of entanglement of this quantum system. Another important goal is to get an approximate estimate of the Von Neumann entropy and check is the back reaction can induce a release of the quantum information in the Hawking radiation.
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