COSMOLOGICAL SINGULARITY
Prof. Vladimir Belinsky
Prof. Vladimir Belinsky
Lecture 1
Sinchronous reference system. Definition of the general solution. Physical and fictitious singularities.
Lecture 2
Kasner solution and its inhomogeneous generalization. Instability
of Kasner dynamics.
Lecture 3
Orthogonal frames. Homogeneous spaces. Bianchi classification.
Lecture 4
Bianchi II model. Transition to the new Kasner regime. Diagonal
Bianchi IX model. Oscillatory regime. Stochasticity.
Lecture 5
Sinchronous reference system. Definition of the general solution. Physical and fictitious singularities.
Lecture 2
Kasner solution and its inhomogeneous generalization. Instability
of Kasner dynamics.
Lecture 3
Orthogonal frames. Homogeneous spaces. Bianchi classification.
Lecture 4
Bianchi II model. Transition to the new Kasner regime. Diagonal
Bianchi IX model. Oscillatory regime. Stochasticity.
Lecture 5
Non-diagonal Bianchi IX model and its inhomogeneous generalization. Rotation of Kasner axis. Orthogonal frame axis. Iwasawa decomposition. Freezing phenomenon.
Lecture 6
Influence of matter. Perfect liquid. Stiff matter state. Scalar field.
Electromagnetic field. Yang-Mills fields.
Lecture 7
Multidimensional space. Pure Gravity.
Lecture 8
Supergravity models. Influence of p-forms and dilatons.
Lecture 9
Cosmological billiard. Coxeter simplex. Kac-Moody Lie algebra.
Hidden symmetry conjecture.
Lecture 10
Dynamical systems approach. Mixmaster attractor.
The course consists of 10 lectures of 60 minutes duration of each
