COSMOLOGICAL SINGULARITY

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

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
blocks_image
Astrophysics, PhD Program