Related papers: Disembodied boundary data for Einstein's equations
Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…
Given asymptotically flat initial data on M^3 for the vacuum Einstein field equation, and given a bounded domain in M, we construct solutions of the vacuum constraint equations which agree with the original data inside the given domain, and…
We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
We present in detail the Einstein equations in the Baumgarte-Shapiro-Shibata-Nakamura formulation for the case of $D$ dimensional spacetimes with $SO(D-d)$ isometry based on a method originally introduced in Ref.1. Regularized expressions…
In this work a new numerical technique to prepare Cauchy data for the initial value problem (IVP) formulation of Einstein's field equations is presented. Directly inspired by the exterior asymptotic gluing (EAG) result of Corvino (2000) our…
We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations. The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data…
We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant…
Errors due to imperfect boundary conditions in numerical relativity simulations of binary black holes can produce unphysical reflections of gravitational waves which compromise the accuracy of waveform predictions, especially for…
A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained…
We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the…
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius…
This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
We study asymptotically flat space-times in 3 dimensions for Einstein gravity near future null infinity and show that the boundary is described by Carrollian geometry. This is used to add sources to the BMS gauge corresponding to a…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
We establish a deformation framework for highly symmetric solutions to the Einstein equations. In this framework, four-dimensional metrics are constructed from three-dimensional {\eta}-Einstein metrics admitting a deformation determined by…
We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various…
The results on the initial boundary value problem for Einstein's vacuum field equation obtained in \cite{friedrich:nagy} rely on an unusual gauge. One of the defining gauge source functions represents the mean extrinsic curvature of the…
For a stationary and axisymmetric spacetime, the vacuum Einstein field equations reduce to a single nonlinear PDE in two dimensions called the Ernst equation. By solving this equation with a {\it Dirichlet} boundary condition imposed along…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…