Related papers: Stability of the Einstein-Lichnerowicz constraints…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
The stability of Einstein static universe against homogeneous scalar perturbations in the context of braneworld scenario is investigated. The stability regions are obtained in terms of the constant geometric linear equation of state…
Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…
We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density…
In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have…
We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…
This survey deals with two closely connected topics: first, the stability of Einstein metrics under the Einstein-Hilbert functional, and second, their deformation theory and the study of the moduli space of Einstein metrics on a compact…
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein…
The conformal method in general relativity aims to successfully parametrise the set of all initial data associated with globally hyperbolic spacetimes. One such mapping was suggested by David Maxwell. I verify that the solutions of the…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
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…
In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-constant mean curvature. In particular, the non-constant mean…
The stability of the Einstein static universe against the homogeneous scalar perturbations in $f(T)$ gravity is analyzed. Both the spatial closed and open universes are considered. We find that the stable Einstein static solutions exist in…
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we…
We re-examine the dynamical stability of the nakedly singular, static, spherical ly symmetric solutions of the Einstein-Klein Gordon system. We correct an earlier proof of the instability of these solutions, and demonstrate that there are…