Related papers: Linear hyperbolic equations in a double null folia…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those…
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.…
In this paper we pursue further a programme initiated in a previous work and aimed at the construction, classification and property investigation of time dependent solutions of supergravity (superstring backgrounds) through a systematic…
Cosmological models of Bianchi type V and I containing a perfect fluid with a linear equation of state plus cosmological constant are investigated using a tetrad approach where our variables are the Riemann tensor, the Ricci rotation…
This paper is devoted to investigate the exact solutions of Bianchi type $I$ spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum tensor $T$. For this…
We introduce a complex pure connection action with constraints which is diffeomorphism and gauge invariant. Taking as an internal group $SU(2)$, we obtain, from the equations of motion, anti-self-dual Einstein spaces together with the zero…
The purpose of this paper is to revisit the Bianchi identities existing for the Riemann and Weyl tensors in the combined framework of the formal theory of systems of partial differential equations (Spencer cohomology, differential systems,…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
In this paper, we solve the field equations in metric f(R) gravity for Bianchi type VI_0 spacetime and discuss evolution of the expanding universe. We find two types of non-vacuum solutions by taking isotropic and anisotropic fluids as the…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
We present a gauge theory of the conformal group in four spacetime dimensions with a non-vanishing torsion. In particular, we allow for a completely antisymmetric torsion, equivalent by Hodge duality to an axial vector whose presence does…
In general relativity, the double null foliation is one for which $d$-dimensional spacetime is foliated by two families of intersecting null hyper surfaces (i.e. surfaces whose normal vectors are null) of $(d-1)$ dimensions. Their…
In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Lambda, but taking into account the effects of a $c$-variable into the curvature tensor. We study the model under the…
We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$…
In the framework of a general scalar-tensor theory, where the scalar field is non-minimally coupled to the five-dimensional Ricci scalar curvature, we investigate the emergence of complete brane-world solutions. By assuming a variety of…
We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm…
In this paper, we prove that the 5-dimensional Schwarzschild-Tangherlini solution of the Einstein vacuum equations is orbitally stable (in the fully non-linear theory) with respect to vacuum perturbations of initial data preserving triaxial…
This paper addresses pure gauge questions in the study of (asymptotically) de Sitter spacetimes. We construct global solutions to the eikonal equation on de Sitter, whose level sets give rise to double null foliations, and give detailed…