Related papers: The 'Regularity Singularity' at Points of General …
We identify a region of F(R)=R^{N} gravity without external sources which is isometric to the spacetime of colliding plane waves (CPW). From the derived curvature sources, N (N>1) measures the strength (i.e. the charge) of the source. The…
The problem of collisions of shockwaves in gravity is well known and has been studied extensively in the literature. Recently, the interest in this area has been revived trough the anti-de-Sitter space/Conformal Field Theory correspondence…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One…
The spherically symmetric Einstein-Vlasov system is considered in Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem is the issue of global existence for initial data without size restrictions. The main purpose…
Regularity theorems are presented for cosmology and gravitational collapse in non-Riemannian gravitational theories. These theorems establish conditions necessary to allow the existence of timelike and null path complete spacetimes for…
We show that the Nariai-Bertotti Petrov type D, homogeneous solution of Einstein's vacuum field equations with a cosmological constant describes the space-time in the interaction region following the head-on collision of two homogeneous,…
A method is given to generate the non-linear interaction (collision) of linearly polarized gravity coupled torsion waves in a non-metric theory. Explicit examples are given in which strong mutual focussing of gravitational waves containing…
We present authors' new theory of the RT-equations, nonlinear elliptic partial differential equations which determine the coordinate transformations which smooth connections $\Gamma$ to optimal regularity, one derivative smoother than the…
In the three-dimensional pure Einstein gravity, the geometries of the vacuum space-times are always trivial, and gravitational waves (gravitons) are strictly forbidden. For the first time, we find a vacuum circularly symmetric black hole…
The junction conditions for general theories of gravity based on actions that depend on arbitrary functions of the curvature scalar invariants (including differential invariants) are obtained using the distributional formalism. In case of…
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static…
We find a self-consistent pp-gravitational shock wave solution to the semiclassical Einstein equations resulting from the $1/N$ approach to the effective action. We model the renormalized matter stress-energy-momentum tensor by $N$ massless…
We consider Einstein gravity extended with Riemann-squared term and construct the leading-order perturbative solution to the rotating black hole with all equal angular momenta in $D=7$. We find that in the extremal limit, the linear…
The existence of black holes in the Universe is nowadays established on the grounds of a blench of astrophysical observations, most notably those of gravitational waves from binary mergers and the imaging of supermassive objects at the…
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
The main results are the following. We derived the matching conditions for the spherically symmetric singular hypersurface (in our case it is equivalent to the world line) in the Weyl$+$Einstein gravity. It was found, that the residual…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
We present a new family of exact solutions of the Einstein equations, constructed through the Khan-Penrose procedure, that may be interpreted as representing the propagation of a pair of solitons, in the background of a plane-wave collision…
Shock wave solutions of the Einstein equations have been constructed in coordinate systems in which the gravitational metric is only Lipschitz continuous, but the connection $\Gamma$ and curvature $Riem(\Gamma)$ are both in $L^{\infty}$. At…