Oscillatory models in general relativity
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.
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