Related papers: Relativistic MHD and black hole excision: Formulat…
This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of Reconstruction-Evolution methods, a standard class of HRSC methods. We test three different…
We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between.…
We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild…
Despite the fact that the Schwarzschild and Kerr solutions for the Einstein equations, when written in standard Schwarzschild and Boyer-Lindquist coordinates, present coordinate singularities, all numerical studies of accretion flows onto…
The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of gamma-ray bursts, requires the solution of the…
The paradigm in which magnetic fields play a crucial role in launching/collimating outflows in many astrophysical objects continues to gain support. However, semi-analytical models including the effect of magnetic fields on the dynamics and…
We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the…
An implicit algorithm for solving the equations of general relativistic hydrodynamics in conservative form in three-dimensional axi-symmetry is presented. This algorithm is a direct extension of the pseudo-Newtonian implicit radiative…
We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for Numerical Relativity, in particular for their use in black hole excision. As an application, we…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing…
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon…
Fallback supernovae and the collapsar scenario for long-gamma ray burst and hypernovae have received considerable interest as pathways to black-hole formation and extreme transient events. Consistent simulations of these scenarios require a…
In this paper, we study the black hole solution of self-similar gravitational collapse in the Einstein-axion-dilaton system for the elliptic class in four dimensions. The solution is invariant under space-time dilation, which is combined…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…