Classical and quantum analysis of 3D electromagnetic pp-wave spacetime

Abstract

The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A classification is presented based on the symmetry group. To the best of our knowledge, the solution corresponding to only one of the Classes is known. The dynamics of some of the Classes was also derived from a minisuperspace Lagrangian which has been constructed. This Lagrangian contains a degree of freedom (the lapse) which can be considered either as dynamical or non-dynamical (indicating a singular or a regular Lagrangian correspondingly). Surprisingly enough, on the space of classical solutions, an equivalence of these two points of view can be established. The canonical quantization is then used in order to quantize the system for both the singular and regular Hamiltonian. A subsequent interpretation of quantum states is based on a Bohm-like analysis. The semi-classical trajectories deviate from the classical only for the regular Hamiltonian and in particular for a superposition of eigenstates (a Gaussian initial state has been used). Thus, the above mentioned equivalence is broken at the quantum level. It is noteworthy that the semi-classical trajectories tend to the classical ones in the limit where the initial wavepacket is widely spread. Hence, even with this simple superposition state, the classical solutions are acquired as a limit of the semi-classical.

arXiv comment27 pages, no figures, updated to match the CQG published version

References in corpus (19)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• The Black Hole in Three Dimensional Space Time
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Penrose limits, supergravity and brane dynamics
• Electromagnetic fields in curved spacetimes
• Conformal Properties of Chern-Simons Vortices in External Fields
• Conformal Properties of Chern-Simons Vortices in External Fields
• Finsler pp-waves
• Time-Dependent Automorphism Inducing Diffeomorphisms In Vacuum Bianchi Cosmologies And The Complete Closed Form Solutions For Type II & V
• Automorphisms and a Cartography of the Solution Space for Vacuum Bianchi Cosmologies: The Type III Case
• Vanishing of the conformal anomaly for strings in a gravitational wave
• Canonical Quantization of the BTZ Black Hole using Noether Symmetries
• All solutions of Einstein's equations in 2+1 dimensions: $\Lambda$-vacuum, pure radiation, or gyratons
• Strings in plane-fronted gravitational waves
• Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes
• Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
• The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)
• PP-waves from rotating and continuously distributed D3-branes
• Geodesic deviation in Kundt spacetimes of any dimension

Cited by in corpus (3)

• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
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• Dynamically equivalent ΛCDM equations with underlying Bianchi Type geometry