Related papers: Weakly decaying asymptotically flat static and sta…
On a given closed connected manifold of dimension two, or greater, we consider the squared $L^2$-norm of the scalar curvature functional over the space of constant volume Riemannian metrics. We prove that its critical points have constant…
We take a step towards characterising stationary data for the vacuum Einstein equations, by finding a necessary condition on initial data for which the evolution is a solution of the vacuum equations admitting a Killing vector, which is…
It is proved that any static system that is spacetime-geodesically complete at infinity, and whose spacelike-topology outside a compact set is that of R^3 minus a ball, is asymptotically flat. The matter is assumed compactly supported and…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
We find constrained instantons in Einstein gravity with and without a cosmological constant. These configurations are not saddle points of the Einstein-Hilbert action, yet they contribute to non-perturbative processes in quantum gravity. In…
We study the defocusing nonlinear Schr\"odinger equation on noncompact metric graphs under general self-adjoint vertex conditions ensuring the existence of a negative eigenvalue of the Hamiltonian operator. First, we focus on the existence…
We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field…
This is the second part of the investigation started in [Stationary solutions and asymptotic flatness I]. We prove here that Strongly Stationary ends having cubic volume growth are Weakly Asymptotically Flat. Combined with the results of…
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…
We determine the electrostatic self-force at rest in an arbitrary static metric with cylindrical symmetry in the linear approximation in the Newtonian constant. In linearised Einstein theory, we express it in terms of the components of the…
The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric…
We consider the Einstein/Yang-Mills equations in $3+1$ space time dimensions with $\SU(2)$ gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is…
We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as…
In contrast to the phenomenon of nullification of the cosmological constant in the equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological…
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a…
In this work we investigate the asymptotic behaviour of solutions to the Einstein equations with a minimally coupled scalar field. The primary focus of the present paper here establishing under what conditions a solution becomes…
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity…
First we review some of the attempts made to find exact spherically symmetric solutions of Einstein field equations in the presence of scalar fields .Wyman solution in both static and non static scalar field is discussed briefly and it is…
Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose…
We prove that every Einstein metric on the unit ball B^4 of C^2, asymptotic to the Bergman metric, is equal to it up to a diffeomorphism. We need a solution of Seiberg--Witten equations in this infinite volume setting. Therefore, and more…