Combining Cauchy and characteristic codes. II. The interface problem for vacuum cylindrical symmetry

Abstract

This paper continues a series investigating methods of combining Cauchy and characteristic techniques in numerical relativity. We present a technique for passing gravitational wave information between an inner Cauchy region and an outer, compactified, characteristic region via a numerical interface. In this developmental work the method is applied to vacuum cylindrical spacetime with two degrees of gravitational freedom. A comparison of our numerical results with an analytic solution, and a number of numerical experiments involving the propagation of Gaussian wave packets, indicate that the techniques presented here can produce very satisfactory results. PACS number(s): 04.

Cauchy-characteristic evolution of Einstein-Klein-Gordon systems

“…The concept of a null exterior attached to a Cauchy evolution appears also in connection with perturbative approaches to the outer boundary problem, e.g., in [19] as well as in [1]. Yet, only recently [9][10][11]4], has the concept been carefully explored with respect to its practicability. A detailed study of the stability and accuracy of CCM for linear and non-linear wave equations has been presented in [4,3], illustrating its potential for a wide range of wave systems.…”

“…A detailed study of the stability and accuracy of CCM for linear and non-linear wave equations has been presented in [4,3], illustrating its potential for a wide range of wave systems. The numerical investigation of cylindrically symmetric solutions of the Einstein equations has also been carried out [10,11].…”

Black hole excision with matching

“…The strategy of matching an interior Cauchy evolution to an exterior outgoing characteristic evolution has been described [19][20][21] and implemented to provide a computational Cauchy outer boundary condition in various cases, ranging from 1 and 2 dimensional simulations [22][23][24][25] to 3-dimensional simulations that include I + [26,27]. A slight modification allows changing an outgoing null formalism (and its evolution code) to an ingoing one.…”

Dynamic cosmic strings. II. Numerical evolution of excited cosmic strings

“…This code performs well in the absence of matter and has been used in paper I to study several cylindrically symmetric vacuum solutions. In paper I we have also given details of the convergence analysis and described the modifications with respect to [7] that lead to long term stability with both gravitational degrees of freedom present. However the CCM code performed less satisfactorily in the evolution of the cosmic string.…”

“…The first is based on the Cauchy-characteristic matching code of Dubal et al [7] and d'Inverno et al [8]. This code performs well in the absence of matter and has been used in paper I to study several cylindrically symmetric vacuum solutions.…”