TY - BOOK ID - 78496256 TI - Oscillatory models in general relativity AU - Russell, Esra AU - Pashaev, O. K. PY - 2018 SN - 3110515229 3110515369 9783110515367 9783110515374 3110515377 9783110515367 3110514958 9783110515220 PB - Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, DB - UniCat KW - Cosmic physics. KW - Oscillations. KW - Stellar oscillations. KW - General relativity (Physics) KW - Relativistic theory of gravitation KW - Relativity theory, General KW - Gravitation KW - Physics KW - Relativity (Physics) KW - Pulsations of stars KW - Stars KW - Stellar pulsations KW - Oscillations KW - Astroseismology KW - Pulsating stars KW - Cycles KW - Fluctuations (Physics) KW - Vibration KW - Space sciences KW - Pulsations UR - https://www.unicat.be/uniCat?func=search&query=sysid:78496256 AB - The 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. ContentsPart I: Dissipative geometry and general relativity theoryPseudo-Riemannian geometry and general relativityDynamics of universe modelsAnisotropic and homogeneous universe modelsMetric waves in a nonstationary universe and dissipative oscillatorBosonic and fermionic models of a Friedman-Robertson-Walker universeTime dependent constants in an oscillatory universe Part II: Variational principle for time dependent oscillations and dissipationsLagrangian and Hamilton descriptionsDamped oscillator: classical and quantum theorySturm-Liouville problem as a damped oscillator with time dependent damping and frequencyRiccati representation of time dependent damped oscillatorsQuantization of the harmonic oscillator with time dependent parameters ER -