Exact Classical and Quantum Solutions for a Covariant Oscillator Near the Black Hole Horizon in Stueckelberg-Horwitz-Piron Theory
arXiv:1901.03970 · doi:10.1016/j.physleta.2019.02.023
Abstract
We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covarience theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg -Horwitz-Piron (SHP) wave equation for a simple harmonic oscilator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonanl and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum according to a quantum number . To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.
arXiv commentAccepted for publication in "Physics Letters A". This paper is dedicated to Prof. Lawrence P. Horwitz. Major revised version, 9 pages, no figure, letter
References in corpus (6)
- Black Holes in Higher Dimensions
- Geometry of Higher-Dimensional Black Hole Thermodynamics
- Instability of higher dimensional charged black holes in the de-Sitter world
- Geometrothermodynamics of higher dimensional black holes
- Geometro-thermodynamics of tidal charged black holes
- Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS