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We show that, given an arbitrary shift, the lapse $N$ can be chosen so that the extrinsic curvature $K$ of the space slices with metric $\overline g$ in arbitrary coordinates of a solution of Einstein's equations satisfies a quasi-linear…
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…
An exact class of solutions of the 5D vacuum Einstein field equations (EFEs) is obtained. The metric coefficients are found to be non-separable functions of time and the extra coordinate $l$ and the induced metric on $l$ = constant…
The question of geodesic completeness of cosmological spacetimes has recently received renewed scrutiny. A particularly interesting result is the observation that the well-known Borde-Guth-Vilenkin (BGV) theorem may misdiagnose geodesically…
We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because…
In this paper, we study the past asymptotics of $(2+1)$-dimensional solutions to the Einstein scalar-field Vlasov system which are close to Friedman-Lema\^itre-Robertson-Walker spacetimes on an initial hypersurface diffeomorphic to a closed…
The expansion of the Universe is accelerating, as testified by observations of supernovae of type Ia as a function of redshift. Explanations are of two types: modifications of Einstein gravity or new forms of energy, coined dark energy.The…
The response of a gravitational wave detector to scalar waves is analysed in the framework of the debate on the choice of conformal frames for scalar-tensor theories. A correction to the geodesic equation arising in the Einstein conformal…
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic, we construct a family of metrics depending on a small…
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In…
In the paper, we have presented a higher-dimensional cosmological model with a generalized Chaplygin-type gas to explain the recent acceleration of the universe. Dimensional reduction is feasible in this model, and our solutions are…
In this paper, we first investigate the mathematical aspects of supersonic flow of a Chaplygin gas past a conical wing with diamond-shaped cross sections in the case of a shock wave detached from the leading edges. The flow under…
When gravitational waves propagate near massive objects, their paths curve resulting in gravitational lensing, which is expected to be a promising new instrument in astrophysics. If the time delay between different paths is comparable with…
In order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as \emph{"Energy-Momentum Squared Gravity"}. The extra terms of the model emerge in the high…
We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. De-localization of mass and charge is due to the presence of…
The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved…
In recent years, strong analogies have been established between the physics of acoustic perturbations in an inhomogeneous dynamical fluid system, and some kinematic features of space-time in general relativity. An effective metric, referred…
We study selected aspects of quantum gravity phenomenology inspired by the gravitational analogy in Bose--Einstein condensates (BECs). We first review the basic ideas and formalism of analogue gravity in BECs, with particular emphasis on…
We study the propagation of super-horizon cosmological perturbations in a non-singular bounce spacetime. The model we consider combines a ghost condensate with a Galileon term in order to induce a ghost-free bounce. Our calculation is…
We construct models of static spherical distributions of perfect fluid in trace--free Einstein gravity theory. The equations governing the gravitational field are equivalent to the standard Einstein's equations however, their presentation…