V. B. Belayev, The dynamics in general relativity theory: variational methods
URSS, Moscow, 2017
The book is mainly used an algebraic approach
to the presentation of the theory of relativity, much attention is paid to the
variational methods and mechanics of motion of particles in the gravitational
field, including the dynamics. The introduction of metrical energy of the light-like particle allows to determine its Lagrangian
and use not only the kinematics, but also the dynamics for the analysis of its
free movement. The problem of energy and momentum transferred to the particle
or system of the gravitational field, for different types of energy and
momentum. An analogy with Newtonian gravity and the
gravitational masses of the photon and material particle are obtained in a weak gravitational field.
Differentiated approach to the conservation laws allows
to determine the pressure of gravity field and vacuum.
This is done on the basis of solutions of Einstein's field equations for a
static spherically symmetric source. The speed of gravity in curved space
obtained by using analogies with the gaseous medium.
The bases of the theory of Kaluza-Klein for a
five-dimensional space-time, the theory of induced gravity is considered.
Models of the rotating hyperspace with space- and time-like fifth coordinate,
dynamics of the material particle in them are investigated.
The book is intended for scientists, graduate students,
undergraduate students majoring in physics and astronomy. As in the first part
contains the basis of the special theory of relativity, it is also of interest
for those who begin to study this branch of physics.
Kerr
Black Hole
Slowly rotating
Rotating at medium speed Fast rotating