Quantum Phenomena Inside a Black Hole: Quantization of the Scalar Field Iniside Horizon in Schwarzschild Spacetime
Pawel Gusin,
Andrzej Radosz,
Andy T. Augousti,
Janos Polonyi,
Oleg B. Zaslavskii,
Romuald J. Ściborski
Affiliations
Pawel Gusin
Department of Quantum Technologies, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
Andrzej Radosz
Department of Quantum Technologies, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
Andy T. Augousti
Faculty of Science, Engineering and Computing, Kingston University London, London KT1 2EE, UK
Janos Polonyi
Centre National de la Recherche Scientifique-Institut Pluridisciplinaire Hubert Curien (CNRS-IPHC), Strasbourg University, 23 r. du Loess BP28, 67037 Strasbourg Cedex 2, France
Oleg B. Zaslavskii
Department of Physics and Technology, Kharkov V. N. Karazin National University, 4 Svoboda Square, 61022 Kharkov, Ukraine
Romuald J. Ściborski
School of Health Sciences, Jaramogi Oginga Odinga University of Science and Technology, Bondo 40601, Kenya
We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.
