Related papers: Series expansions and sudden singularities
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which…
A string-inspired duality symmetry of the spatially flat Friedmann equations of general-relativistic cosmology is discussed and generalized, providing a map between exact solutions corresponding to different values of the barotropic index.
An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing…
Assuming that the Universe is filled by one single fluid, we present in the context of General Relativity a possible explanation for the acceleration of the Universe. We use ordinary thermodynamics and the fact that small matter…
We present an exact solution to the equations of massive gravity that displays cosmological constant-like behavior for any spherically symmetric distribution of matter, including arbitrary time dependence. On this solution, the new degrees…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a non-singular cosmological…
In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density…
The general solution of the gravitational field equations for a full causal bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density to the power 1/4, is obtained in the flat…
We construct a large family of exact solutions to the hyperbolic system of 3 equations of ideal granular hydrodynamics in several dimensions for arbitrary adiabatic index $\gamma$. In dependence of initial conditions these solutions can…
We obtain the analytic solution of the Friedmann equation for fully realistic cosmologies including radiation, non-relativistic matter, a cosmological constant $\lambda$ and arbitrary spatial curvature $\kappa$. The general solution for the…
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation.…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to…
We investigate the gravitational field of a kinetic gas beyond its usual derivation from the second moment of the one-particle distribution function (1PDF), that serves as energy-momentum tensor in the Einstein equations. This standard…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann…
We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is…
On a bounded smooth domain we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to the boundary of the domain. We derive global a priori bounds of the…
We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden…