Related papers: Toward computing gravitational initial data withou…
When using the black hole exclusion (horizon boundary condition) technique, $K$ is usually nonzero and spatially variable, so none of the special cases of York's conformal-decomposition algorithm apply, and the full 4-vector nonlinear York…
Numerical relativity simulations provide a means by which to study the evolution and end point of strong over-densities in cosmological spacetimes. Specific applications include studies of primordial black hole formation and the robustness…
In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…
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 evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
In this paper we present new stability and optimal error analyses of hybridized discontinuous Galerkin (HDG) methods which do not require elliptic regularity assumptions. To obtain error estimates without elliptic regularity assumptions, we…
We study here the spherical gravitational collapse assuming initial data to be necessarily smooth, as motivated by the requirements based on physical reasonableness. A tangential pressure model is constructed and analyzed in order to…
The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
A general relativistic, stationary and axisymmetric black hole in a four-dimensional asymptotically-flat spacetime is fully determined by its mass, angular momentum and electric charge. The expectation that astrophysically relevant black…
We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R^3 for the nonsingular part of the metric conformal factor. With this approach we can…
In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of…
A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly…
The Einstein evolution equations have been written in a number of symmetric hyperbolic forms when the gauge fields--the densitized lapse and the shift--are taken to be fixed functions of the coordinates. Extended systems of evolution…
We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal…
In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…
We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of…
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent…
The construction of constraint-satisfying initial data is an essential element for the numerical exploration of the dynamics of compact-object binaries. While several codes have been developed over the years to compute generic…