The parabolic-hyperbolic formulation of the initial data of the Einstein equations for multiple black holes systems has been proposed recently [1-3]. It provides an alternative to the traditional conformal method [4]. During the talk, a numerical implementation of the approach to the initial data problem of general relativity will be presented. It will involve black holes described by a metric...

Abstract: Already in the 30s, Schroedinger observed that all null Maxwell fields solve the equations for the electromagnetic field in any non-linear electrodynamics. More generally, we study properties of “universal” p-forms, i.e., electromagnetic fields that solve simultaneously any generalized electrodynamics (for which the field equations contain arbitrary powers and...

We present a modified method of investigation of particle content of a metric theory of gravitation whose Lagrangian explicitly depends on the Weyl tensor. Without any resort to observations we consider the problem from purely field–theoretical viewpoint. We apply the tenet of field theory that each classical field should correspond to a quantum particle with definite mass and spin and...

We review some recent results concerning inflationary scenario in the framework of Starobinski-Palatini FLRW cosmology, which can be reduced to the two-dimensional singular (piecewise-smooth) dynamical system of Newtonian type. Therefore, it can be describe in geometric terms of the corresponding potential function. Analytical calculations are given for the case with dust matter and...

The lack of external and fixed time is encoded into the canonical formalism of general relativity by means of the Hamiltonian constraint. The lack of time does not imply the lack of evolution but rather brings to the fore the role of internal clocks which are some largely arbitrary internal degrees of freedom with respect to which the evolution of timeless systems can be described. I will take...