18 research outputs found
Shapovalov wave-like spacetimes
A complete classification of space-time models is presented, which admit the
privileged coordinate systems, where the Hamilton-Jacobi equation for a test
particle is integrated by the method of complete separation of variables with
separation of the isotropic (wave) variable, on which the metric of space
depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces,
exact solutions of the Einstein equations with a cosmological constant in
vacuum are found. Complete integrals are presented for the eikonal equation and
the Hamilton-Jacobi equation of motion of test particles.Comment: 17 page
Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe
For the Bianchi type VI universe, exact solutions of the equation of geodesic
deviation in a strong primordial gravitational wave in a privileged coordinate
system are obtained. The solutions refer to Shapovalov's gravitational-wave
models of spacetime and allow the existence of complete integrals of the
Hamilton-Jacobi equation for test particles. For all the solutions obtained,
the analytical form of the tidal acceleration vector in a strong primordial
gravitational wave is obtained. An explicit form of the coordinate
transformation, an explicit form of the metric of the primordial gravitational
wave of the Bianchi type VI universe, and the form of the tidal acceleration
vector in the laboratory synchronous coordinate system are obtained. The
synchronous coordinate system is associated with a freely falling observer and
allows the observer to separate time and spatial coordinates, as well as to
synchronize time at different points in space. The presented mathematical
approach can be applied both in the general theory of relativity and in
modified theories of gravity.Comment: 26 page
An Exact Model of a Gravitational Wave in the Bianchi III Universe Based on Shapovalov II Wave Spacetime and the Quadratic Theory of Gravity
Exact models of primordial gravitational waves in the Bianchi type-III universe were constructed on the basis of the quadratic theory of gravity with a scalar field and pure radiation in Shapovalov wave spacetimes of type II (subtype 2). Exact solutions of the field equations and scalar equation were obtained. The characteristics of pure radiation were determined. An explicit form of the scalar field functions included in the Lagrangian of the considered quadratic theory of gravity was found. The trajectories of the propagation of light rays in the considered gravitational wave models were obtained
Type I Shapovalov Wave Spacetimes in the Brans–Dicke Scalar-Tensor Theory of Gravity
Exact solutions for Shapovalov wave spacetimes of type I in Brans–Dicke’s scalar-tensor theory of gravity are constructed. Shapovalov wave spacetimes describe gravitational wave models that allow for the the separation of wave variables in privileged coordinate systems. In contrast to general relativity, the vacuum field equations of the Brans–Dicke scalar-tensor theory of gravity lead to exact solutions for type I Shapovalov spaces, allowing for the the construction of observational tests to detect such wave disturbances. Furthermore, the equations for the trajectories of the test particles are obtained for the models considered