Oscillatory models in general relativity
type: Item
instance of: scholarly article
title: Oscillatory models in general relativity
zbMATH Open document ID: 1414.83002
DOI: 10.1515/9783110515367
author: Esra Russell
author: Oktay K. Pashaev
published in: De Gruyter Studies in Mathematical Physics
publication date: 2017-10-13T00:00:00Z
review text: This books deals with homogeneous cosmologies in general relativity both isotropic and anisotropic, and the connection of their dynamics and quantization with those of the time dependent harmonic oscillator. Chapter 1 is a review of general relativity. Chapter 2 discusses isotropic and homogeneous cosmologies. Chapter 3 introduces anisotropies in the homogeneous models. Chapter 4 deals with the linearization of the Einstein equations to discuss gravitational waves and introduce the connection with harmonic oscillators. Chapter 5 discusses bosonic and fermionic modes of the Friedmann-Robertson-Walker cosmologies. Chapter 6 considers oscillatory cosmologies with time dependent gravitational and cosmological constants. The second part of the book is devoted to the variational and Hamiltonian description of time-dependent harmonic oscillators. Chapter 7 works out the Poisson brackets and Hamilton's equations. Chapter 8 considers dissipation and damped harmonic oscillators and their time dependent Hamiltonians. Oscillators with time dependent mass are considered and the Caldirola-Kanai Hamiltonian is covered. Chapter 9 considers two formulations of the damped harmonic oscillator with time depending damping and frequency and their relation to the self-adjoint extension of the Sturm-Liouville problem. Chapter 10 considers some special cases with the Riccati representation of the special functions as oscillator-type problems. Chapter 11 considers the quantization of time dependent damped oscillators.
reviewed by: Jorge Pullin
Mathematics Subject Classification ID: 83-02
Mathematics Subject Classification ID: 83F05
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 00A79
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 70H40
zbMATH DE Number: 6790769
zbMATH Keywords: cosmology
zbMATH Keywords: harmonic oscillators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/9783110515367
OpenAlex ID: W2768118926
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description: scientific article