Related papers: A large data result for vacuum Einstein's equation…
In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant ($\Lambda$) but without matter fields. We have found that the classical solutions of…
In this study, we consider three dark energy models in which $\Lambda$ is not constant, but has a dynamic nature that depends on the Hubble parameter $H$ and/or its time derivative $\dot{H}$. We analyze the generalized running vacuum model,…
For the physical vacuum free boundary problem with the sound speed being $C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous near vacuum boundaries of the three-dimensional compressible Euler equations with damping, the global existence of…
Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
Despite the ultraviolet problems with canonical quantum gravity, as an effective field theory its infrared phenomena should enjoy fully quantum mechanical unitary time evolution. Currently this is not possible, the impediment being what is…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…
In this paper we perform a systematic study of spatially flat $[(3+D)+1]$-dimensional Einstein-Gauss-Bonnet cosmological models with $\Lambda$-term. We consider models that topologically are the product of two flat isotropic subspaces with…
We consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak solutions using a combination of a priori estimates for the…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The…
A cosmological model describing the evolution of $n$ Einstein spaces $(n>1)$ with $m$-component perfect-fluid matter is considered. When all spaces are Ricci-flat and for any $\alpha$-th component the pressures in all spaces are…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive,…
This paper is concerned exclusively with axisymmetric spacetimes. We want to develop reductions of Einstein's equations which are suitable for numerical evolutions. We first make a Kaluza-Klein type dimensional reduction followed by an ADM…
The cosmological constant (lambda) of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional theory of the type needed for unification. The exact 5D solution for lambda less than 0 shows waves in…
The cosmological constant term, $\Lambda$, in Einstein's equations has been for three decades a building block of the concordance or standard $\Lambda$CDM model of cosmology. Although the latter is not free of fundamental problems, it…
This study focuses on the impact of the cosmological constant on hyperbolically symmetric matter configurations in static background. We extend the work of Herrera \cite{herrera2021hyperbolically} and describe the influences of such…
Next year we will celebrate 100 years of the cosmological term, $\Lambda$, in Einstein's gravitational field equations, also 50 years since the cosmological constant problem was first formulated by Zeldovich, and almost about two decades of…
We show that any homogeneous initial data set with $\Lambda<0$ on a product 3-manifold of the orthogonal form $(F\times \mathbb S^1,a_0^2dz^2+b_0^2\sigma^2,c_0dz^2+d_0\sigma)$, where $(F,\sigma)$ is a closed 2-surface of constant curvature…