Related papers: Hyperboloidal evolution with the Einstein equation…
In view of late-time cosmic acceleration, a dark energy cosmological model is revisited wherein Einstein's cosmological constant is considered as a candidate of dark energy. Exact solution of Einstein field equations (EFEs) is derived in a…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
We present a uniform (and unambiguous) procedure for scaling the matter fields in implementing the conformal method to parameterize and construct solutions of Einstein constraint equations with coupled matter sources. The approach is based…
We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…
The problem is solved of describing scale factors of a homogeneous isotropic spaces-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled…
We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein…
The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…
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 article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
Einstein's equations for general relativity, when viewed as a dynamical system for evolving initial data, have a serious flaw: they cannot be proven to be well-posed (except in special coordinates). That is, they do not produce unique…
The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
In this paper we propose that the accelerating expansion of the present matter-dominated universe, as suggested by the recent distance measurements of type Ia supernovae, is generated along with the evolution of space in extra dimensions.…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…