{"product_id":"9783110514957","title":"Oscillatory Models in General Relativity (De Gruyter Studies in Mathematical Physics)","description":"\u003cp\u003eThe book employs oscillatory dynamical systems to represent the Universe mathematically via constructing classical and quantum theory of damped oscillators. It further discusses isotropic and homogeneous metrics in the Friedman-Robertson-Walker Universe and shows their equivalence to non-stationary oscillators. The wide class of exactly solvable damped oscillator models with variable parameters is associated with classical special functions of mathematical physics. Combining principles with observations in an easy to follow way, it inspires further thinking for mathematicians and physicists. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eContents\nPart I: Dissipative geometry and general relativity theory\nPseudo-Riemannian geometry and general relativity\nDynamics of universe models\nAnisotropic and homogeneous universe models\nMetric waves in a nonstationary universe and dissipative oscillator\nBosonic and fermionic models of a Friedman-Robertson-Walker universe\nTime dependent constants in an oscillatory universe \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003ePart II: Variational principle for time dependent oscillations and dissipations\nLagrangian and Hamilton descriptions\nDamped oscillator: classical and quantum theory\nSturm-Liouville problem as a damped oscillator with time dependent damping and frequency\nRiccati representation of time dependent damped oscillators\nQuantization of the harmonic oscillator with time dependent parameters \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eEsra Russel\u003c\/strong\u003e, New York University Abu Dhabi, United Arab Emirates, \u003cstrong\u003eOktay Pashaev\u003c\/strong\u003e, Izmir Institute of Technology, Turkey \u003c\/p\u003e \u003cp\u003eTable of content:\nChapter 1 Introduction\nPart I Dissipative Geometry and General Relativity Theory\nChapter 2 Pseudo-Riemannian Geometry and General Relativity\n2.1. Curvature of Space Time and Einstein Field Equations\n2.1.1. Einstein Field Equations\n2.1.2. Energy Momentum Tensor\n2.2. Universe as a Dynamical System\n2.2.1. Friedman-Robertson-Walker (FRW) Metric\n2.2.2. Friedman Equations\n2.2.3. Adiabatic Expansion and Friedman Differential Equation\nChapter 3 Dynamics of Universe Models\n3.1. Friedman Models\n3.1.1. Static Models\n3.1.2. Empty Models\n3.1.3. Three Non-Empty Models with ¤ = 0\n3.1.4. Non-Empty Models with ¤ 6= 0\n3.2. Milne Model\nChapter 4 Anisotropic and Homogeneous Universe Models\n4.1. General Solution\n4.1.1. Constant Density and Zero Pressure\n4.1.2. Constant Pressure and Zero Density\n4.1.3. Absence of Pressure and Density\nChapter 5 Barotropic Models of FRW Universe\n5.1. Bosonic FRW Model\n5.2. Fermionic FRW Barotropy\n5.3. Decoupled Fermionic and Bosonic FRW Barotropies\n5.4. Coupled Fermionic and Bosonic Cosmological Barotropies\nChapter 6 Time Dependent Gravitational and Cosmological Constants\n6.1. Model and Field Equation\n6.2. Solution of the Field Equation\n6.2.1. G (t) ~ H\n6.2.1.1. Inflationary Phase\n6.2.1.2. Radiation Dominated Phase\n6.2.2. G (t) ~ 1\/H\n6.2.2.1. Inflationary Phase\n6.2.2.2. Radiation Dominated Phase\nChapter 7 Gravitational Waves in Non-Stationary Universe and Dissipative Oscillator\n7.1. Linear Gravitational (Metric) Waves in Flat Space Time\n7.2. Linear Gravitational (Metric) Waves in Non-Stationary Universe\n7.2.1. Hyperbolic Geometry of Damped Oscillator and Double Universe\nPart II Variational Principles for Time Dependent Oscillations and Dissipations\nChapter 8 Lagrangian and Hamilton Description\n8.1. Generalized Co-ordinates and Velocities\n8.2. Principle of Least Action\n8.3. Hamilton's Equations\n8.3.1. Poisson Brackets\nChapter 9 Damped Oscillator: Classical Quantum\n8.4. Damped Oscillator\n8.5. Bateman Dual Description\n8.6. Caldirola Kanai Approach for Damped Oscillator\n8.7. Quantization of Caldirola-Kanai Damped Oscillator with Constant Frequency and Constant Damping\nChapter 10 Sturm Liouville Problem as Damped Parametric Oscillator\n10.1. Sturm Liouville Problem in Doublet Oscillator Representation and Self-Adjoint Form\n10.1.1. Particular Cases for Non-Self Adjoint Equation\n10.1.2. Variational Principle for Self Adjoint Operator\n10.1.3. Particular Cases for Self Adjoint Equation\n10.2. Oscillator Equation with Three Regular Singular Points\n10.2.1. Hypergeometric Functions\n10.2.2. Confluent Hypergeometric Function\n10.2.3. Bessel Equation\n10.2.4. Legendre Equation\n10.2.5. Shifted-Legendre Equation\n10.2.6. Associated-Legendre Equation\n10.2.7. Hermite Equation\n10.2.8. Ultra-Spherical (Gegenbauer) Equation\n10.2.9. Laguerre\n10.2.10. Associated Laguerre Equation\n10.2.11. Chebyshev Equation I\n10.2.12. Chebyshev Equation II\n10.2.13. Shifted Chebyshev Equation I\nChapter 11 Riccati Representation of Time Dependent Damped Oscillators\n11.1. Hypergeometric Equation\n11.2. Confluent Hypergeometric Equation\n11.3. Legendre Equation\n11.4. Associated-Legendre Equation\n11.5. Hermite Equation\n11.6. Laguerre Equation\n11.7. Associated Laguerre Equation\n11.8. Chebyshev Equation I\n11.9. Chebyshev Equation II\nChapter 12 Conclusion\nReferences\nList of Tables\nAppendices\nAppendix A Preliminaries for Tensor Calculus\nA.1. Tensor Calculus\nA.2. Calculating Christoffel Symbols from Metric\nA.3. Parallel Transport and Geodesics\nA.4. Variational Method for Geodesics\nA.5. Properties of Riemann Curvature Tensor\nA.6. Bianchi Identities; Ricci and Einstein Tensors\nA.6.1. Ricci Tensor\nA.6.2. Einstein Tensor\nAppendix B Riccati Differential Equation\nAppendix C Hermited Differential Equation\nC.1. Orthogonality\nC.2. Even\/Odd Functions\nC.3. Recurrence Relation\nC.4. Special Results\nAppendix D Non-Stationary Oscillator Representation of FRW Universe\nD.1. Time Dependent Oscillator\nD.1.1. Delta Function Potential\nAppendix E Bianchi Model: An Alternative Way to Model the Present-Day Universe\nE.1. BI Models\nE.2. Isotropization of BI models into FRW Universe\nE3. Evolution of anisotropic deviations from FRW in decoupling\nE3.1 Isotropization criteria of the radiation and matter dominated BI model\nIndexing \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":45537275019343,"sku":"00000_00000_00000_00000","price":6195.0,"currency_code":"TWD","in_stock":true}],"url":"https:\/\/kinokuniya.com.tw\/products\/9783110514957","provider":"Books Kinokuniya Taiwan","version":"1.0","type":"link"}