The singularity in Hawking and Turok’s model of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of “no-boundary” solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action...

An elliptical invisible cloak is proposed using a coordinate transformation in the ellipticalcylindrical coordinate system, which crushes the cloaked object to a line segment instead of a point. The elliptical cloak is reduced to a nearly-circular cloak if the elliptical focus becomes very small. The advantage of the proposed invisibility cloak is that none of the parameters is singular and the...

We discuss whether the future extrapolation of the present cosmological state may lead to a singularity even in case of “conventional” (negative) pressure of the dark energy field, namely w = p/ρ ≥ −1. The discussion is based on an often neglected aspect of scalar-tensor models of gravity: the fact that different test particles may follow the geodesics of different metric frames, and the need f...

We " explain " , using a Classical approach, how the Universe was created out of " nothing " ,i.e., with no input of initial energy nor mass. The inflationary phase, with exponential expansion, is accounted for, automatically , by our equation of state for the very early Universe. This is a Universe with no-initial infinite singularity of energy density.

This is a survey on our work generalizing the classical Dehn-Sommerville equations (analogous to Poincaré duality, see [10]) for f -vectors of triangulations of manifolds without boundary to general polyhedra. Our key observation is that the exact data needed for the generalization is the classification of points of polyhedra by the Euler characteristics of their links. From this viewpoint, a p...

We investigate collocation methods for the efficient solution of singular boundary value problems with an essential singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to...

We study the formation of central naked singularities in spherical dust collapse with a cosmological constant. We find that the central curvature singularity is locally naked, Tipler strong, and generic, in the sense that it forms from a non-zero-measure set of regular initial data. We also find that the Weyl and Ricci curvature scalars diverge at the singularity, with the former dominating ove...

We consider different aspects of the problem of cosmological singularity such as the BKL oscillatory approach to singularity, the new features of the cosmological dynamics in the neighbourhood of the singularity in multidimensional and superstring cosmological models and their connections with such a modern branch of mathematics as infinite-dimensional Lie algebras. Besides, we consider some ne...

The nature of the initial singularity in spatially compact plane symmetric scalar field cosmologies is investigated. It is shown that this singularity is crushing and velocity dominated and that the Kretschmann scalar diverges uniformly as it is approached. The last fact means in particular that a maximal globally hyperbolic spacetime in this class cannot be extended towards the past through a ...

We discuss the singularity in the Borel plane of the ultraviolet renormalon due to the multiple exchanges of the all-order Gell-Man–Low effective charges. A consistent picture of the UV renormalon emerges when the effective charge is considered in all orders. Contrary to the case of the one-loop effective charge, the strength of the singularity is independent of the number of exchanges. A syste...