Related papers: Exploring the Conformal Constraint Equations
We reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in…
In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…
We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of space-times.
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
This article is dedicated to solving the Einstein constraint equations with apparent horizon boundaries and freely specified mean curvature. The main novelty is that we study the conformal constraint equations assuming only low regularity.
We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions…
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
An outstanding question lying at the core of the AdS/CFT correspondence in string theory is the holographic prescription problem for Einstein metrics, which asserts that one can slightly perturb the conformal geometry at infinity of the…
The Kasner metrics are among the simplest solutions of the vacuum Einstein equations, and we use them here to examine the conformal method of finding solutions of the Einstein constraint equations. After describing the conformal method's…
In relation to the BSSN formulation of the Einstein equations, we write down the boundary conditions that result from the vanishing of the projection of the Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up a…
The Einstein constraint equations have been the subject of study for more than fifty years. The introduction of the conformal method in the 1970's as a parameterization of initial data for the Einstein equations led to increased interest in…
The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a…
To explore possibilities of avoiding coincidence problem in $f(R)$ gravity we consider models in Einstein conformal frame which are equivalent to Einstein gravity with a minimally coupled scalar field. As the conformal factor determines the…
In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations…
An important problem is to determine under which circumstances a metric on a conformally compact manifold is conformal to a Poincar\'e--Einstein metric. Such conformal rescalings are in general obstructed by conformal invariants of the…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…
We make use of the metric version of the conformal Einstein field equations to construct anti-de Sitter-like spacetimes by means of a suitably posed initial-boundary value problem. The evolution system associated to this initial-boundary…
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…