An Inhomogeneous Space–Time Patching Model Based on a Nonlocal and Nonlinear Schrödinger Equation

2016/05/04 by Christine C. Dantas · 9 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Consistency (knowledge bases) #Cosmology #Cosmology and Gravitation Theories #Dynamics (music) #Integrable system #Noncommutative and Quantum Gravity Theories #Nonlinear system #Quantum #gr-qc

paper · pdf · doi:10.1007/s10701-016-0019-6

published in Foundations of Physics 46(10), 1269-1292 (Springer Science+Business Media) · 29 pages, 2 figures, accepted for publication in Foundations of Physics

arxiv created 2016/05/04 · openalex publication_date 2016/05/21 · openalex created_date 2016/06/24 · arxiv updated 2016/06/29 · openalex updated_date 2026/08/05

Abstract

We consider an integrable, nonlocal and nonlinear, Schrödinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Dynamical eigenfunctions and critical density in loop quantum cosmology
• Quantum cosmology: a review
• New connections between moving curves and soliton equations
• The reality conditions for the new canonical variables of general relativity
• Loop quantum cosmology and inhomogeneities
• An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains