Related papers: Initial Conditions for Numerical Relativity -- Int…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each…
The optical appearance of the numerically black hole solutions within the higher derivative gravity illuminated by an accretion disk context is discussed. We obtain solutions for non-Schwarzschild black holes with r0 = 1, r0 = 2, and r0 =…
The main goal of numerical relativity is the long time simulation of highly nonlinear spacetimes that cannot be treated by perturbation theory. This involves analytic, computational and physical issues. At present, the major impasses to…
Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…
This paper is devoted to the computation of compact binaries composed of one black hole and one neutron star. The objects are assumed to be on exact circular orbits. Standard 3+1 decomposition of Einstein equations is performed and the…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
These are the notes for a series of Numerical Study group meetings, held in Lorentz institute in the fall of 2017. The aim of the notes is to provide a non-specialist with the minimal knowledge in numerical methods used in BVP for PDEs,…
We present details of a new numerical code designed to study the formation and evaporation of 2-dimensional black holes within the CGHS model. We explain several elements of the scheme that are crucial to resolve the late-time behavior of…
We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
The modelling of unequal mass binary black hole systems is of high importance to detect and estimate parameters from these systems. Numerical relativity (NR) is well suited to study systems with comparable component masses, $m_1\sim m_2$,…
Black holes, first found as solutions of Einstein's General Relativity, are important in astrophysics, since they result from the gravitational collapse of a massive star or a cluster of stars, and in physics since they reveal properties of…
This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
Electromagnetic observations have been used over the past decades to understand the nature of black holes and the material around them. Our ability to learn about the fundamental physics relies on our understanding of two key ingredients in…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this…