Related papers: Novel finite-differencing techniques for numerical…
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 describe a simple implementation of black hole excision in 3+1 numerical relativity. We apply this technique to a Schwarzschild black hole with octant symmetry in Eddington-Finkelstein coordinates and show how one can obtain accurate,…
We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based…
We present an overview of recent developments in numerical relativity studies of higher dimensional spacetimes with a focus on time evolutions of black-hole systems. After a brief review of the numerical techniques employed for these…
We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which…
Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented.…
The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for Numerical Relativity. New numerical ingredients are presented which avoid gauge pathologies and…
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.…
Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations…
Though the main applications of computer simulations in relativity are to astrophysical systems such as black holes and neutron stars, nonetheless there are important applications of numerical methods to the investigation of general…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before…
I describe approaches to the study of black hole spacetimes via numerical relativity. After a brief review of the basic formalisms and techniques used in numerical black hole simulations, I discuss a series of calculations from axisymmetry…
We evolve a scalar field in a fixed Kerr-Schild background geometry to test simple $(3+1)$-dimensional algorithms for singularity excision. We compare both centered and upwind schemes for handling the shift (advection) terms, as well as…
In this work we explore a numerical technique, based on the spherical harmonic decomposition and the discretization of the radial coordinate through \v{C}eby\v{s}\"ev polynomial interpolation, for the computation of quasi-bound states of…
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…
It is expected that the realization of a convergent and long-term stable numerical code for the simulation of a black hole inspiral collision will depend greatly upon the construction of stable algorithms capable of handling smooth and,…