相关论文: Modeling the Black Hole Excision Problem

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 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…

In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…

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…

Simulations of binary black hole systems using the Spectral Einstein Code (SpEC) are done on a computational domain that excises the regions inside the black holes. It is imperative that the excision boundaries are outflow boundaries with…

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…

We extend previous work on 3D black hole excision to the case of distorted black holes, with a variety of dynamic gauge conditions that are able to respond naturally to the spacetime dynamics. We show that the combination of excision and…

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,…

The scattering process of a dynamic perturbation impinging on a draining-tub model of an acoustic black hole is numerically solved in the time domain. Analogies with real black holes of General Relativity are explored by using recently…

We present a new pseudo-spectral code for the simulation of evolution systems that are second order in space. We test this code by evolving a non-linear scalar wave equation. These non-linear waves can be stably evolved using very simple…

We provide a detailed analysis of several aspects of the turduckening technique for evolving black holes. At the analytical level we study the constraint propagation for a general family of BSSN-type formulation of Einstein's field…

We present long term evolutions of a single black hole of mass $M$ with the BSSN system using pseudospectral methods. For our simulations we use the SGRID code where the BSSN system is implemented in its standard second order in space form.…

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…

In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface…

We present a new method for treating the inner Cauchy boundary of a black hole spacetime by matching to a characteristic evolution. We discuss the advantages and disadvantages of such a scheme relative to Cauchy-only approaches. A prototype…

This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…

Worldtube excision is a method of reducing computational burden in Numerical Relativity simulations of binary black holes in situations where there is a good analytical model of the geometry around (one or both of) the objects. Two such…

When using black hole excision to numerically evolve a black hole spacetime with no continuous symmetries, most 3+1 finite differencing codes use a Cartesian grid. It's difficult to do excision on such a grid, because the natural $r =…

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…

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…