相关论文: The initial state of generalized radiation univers…
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…
In this work, we study cosmological spacetime configurations in $f(Q)$ gravity with nonvanishing symmetric teleparallel connections. It is known that the spatially flat, homogeneous and isotropic connections can be classified into three…
We derive a class of regular black holes from the proper-time renormalization group approach to asymptotically safe gravity. A central challenge is the robustness of physical predictions to the regularization scheme. We address this by…
In this paper, the gravitational field equations for static spherically symmetric perfect fluid models with a polytropic equation of state, $p=k\rho^{1+1/n}$, are recast into two complementary 3-dimensional {\it regular} systems of ordinary…
We show global asymptotic stability of solitary waves of the nonlinear Schr\"odinger equation in space dimension 1. Furthermore, the radiation is shown to exhibit long range scattering if the nonlinearity is cubic at the origin, or standard…
The Einstein static (ES) state is a good candidate for describing the very early universe in terms of a regular cosmological model in which the Big Bang singularity is avoided. In the present study we propose an ES solution in the framework…
We show that generically the initial singularity is isotropic in spatially homogeneous cosmological models in the brane-world scenario. We then argue that it is plausible that the initial singularity is isotropic in typical brane world…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequency and at non-zero frequencies, which correspond to the cases…
We consider Lorentzian General Relativity in a cavity with a timelike boundary, with conformal boundary conditions and also a generalization of these boundary conditions. We focus on the linearized gravitational dynamics about the static…
Recently the first example of a unitary theory of Lorentz-invariant massive gravity allowing for stable self-accelerating de Sitter solutions was found, extending the quasidilaton theory. In this paper we further generalize this new action…
The resolution of the problem of cosmological singularity in the framework of gauge theories of gravitation is discussed. Generalized cosmological Friedmann equations for homogeneous isotropic models filled by interacting scalar fields and…
We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $\Lambda$. This first paper is concerned with the case of $\Lambda =0$. Our approach is fully based on…
The initial state of the spherical gravitational collapse in general relativity has been studied with different methods, especially by using {\it a priori} given equations of state that describe the matter as a perfect fluid. We propose an…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is…
A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that…
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor…