Related papers: Elliptica: a new pseudo-spectral code for the cons…
We present a novel implicit numerical implementation of the parabolic-hyperbolic formulation of the constraints of general relativity. The proposed method is unconditionally stable, has the advantage of not requiring the imposition of any…
Black hole binaries on non-eccentric orbits form an important subclass of gravitational wave sources, but it is a non-trivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute…
Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasi-equilibrium configurations and dynamical evolutions. In this article, we construct quasi-equilibrium configurations for…
The standard approach to initial data for both analytic and numerical computations of black hole collisions has been to use conformally-flat initial geometry. Among other advantages, this choice allows the simple superposition of holes with…
Isolated horizon conditions enforce the time invariance of both the intrinsic and the extrinsic geometry of a (quasilocal) black hole horizon. Nonexpanding horizons, only requiring the invariance of the intrinsic geometry, have been…
Motivated by a geometric understanding of the angular velocity of a Kerr black hole in terms of a quasi-conformal map that describes a 2d Beltrami fluid flow, a new way to construct initial data sets for binary rotating black holes by…
We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two…
We develop a method to compute low-eccentricity initial data of black hole--neutron star binaries in the puncture framework extending previous work on other types of compact binaries. In addition to adjusting the orbital angular velocity of…
GRTresna is a multigrid solver designed to solve the constraint equations for the initial data required in numerical relativity simulations. In particular, it is focussed on scenarios with fundamental fields around black holes and…
In numerical evolutions of binary black holes (BBH) it is desirable to easily control the orbital eccentricity of the BBH, and the number of orbits completed by the binary through merger. This paper presents fitting formulae that allow to…
We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a…
An orbiting black hole binary will generate strong gravitational radiation signatures, making these binaries important candidates for detection in gravitational wave observatories. The gravitational radiation is characterized by the orbital…
We propose a new approach, based on the puncture method, to construct black hole initial data in the so-called trumpet geometry, i.e. on slices that asymptote to a limiting surface of non-zero areal radius. Our approach is easy to implement…
We present a new numerical code developed for the evolution of binary black-hole spacetimes using different initial data and evolution techniques. The code is demonstrated to produce state-of-the-art simulations of orbiting and inspiralling…
We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral…
Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…
Near-Kerr black hole initial datasets are constructed by applying either the parabolic-hyperbolic or the algebraic-hyperbolic form of the constraints. In both cases, strongly and weakly asymptotically flat initial datasets with desirable…
We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays…
We develop a new $C^{\,0}$-continuous Petrov-Galerkin spectral element method for one-dimensional fractional elliptic problems of the form ${}_{0}{\mathcal{D}}_{x}^{\alpha} u(x) - \lambda u(x) = f(x)$, $\alpha \in (1,2]$, subject to…
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…