Excising das All: Evolving Maxwell waves beyond scri

Abstract

We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity. We exploit this freedom to ensure that all light cones are tilted outward in a region near null infinity, which allows us to impose excision-style boundary conditions in our finitedifference code. In this preliminary study we consider electromagnetic waves propagating in a static, conformally compactified spacetime.

Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

“…Moncrief presented the first explicit construction of a hyperboloidal scri-fixing gauge for Minkowski spacetime [72] (for numerical implementations see [73][74][75]). The application of the method in black-hole spacetimes proved to be difficult [76][77][78][79][80], until the general construction of suitable hyperboloidal scri-fixing coordinates on asymptotically flat spacetimes has been presented [81]. Since then, hyperboloidal scri-fixing coordinates have been employed in a rich variety of problems concerning black-hole spacetimes [22,[82][83][84][85][86][87][88][89][90][91].…”

Hyperboloidal evolution of test fields in three spatial dimensions

“…Cuts of future null infinity naturally have spherical topology. Previous studies of hyperboloidal compactification with Cartesian grids report spurious reflections of outgoing signals through null infinity [15]. Therefore this technical requirement may be a limiting factor for applying the hyperboloidal method in numerical codes employing Cartesian grids.…”

“…The gauge parameters in our coordinatization of the conformal Schwarzschild spacetime in a CMC foliation (15) are the coordinate location of null infinity, S, the mean extrinsic curvature of the hyperboloidal surfaces, K, and an integration parameter C that influences the causal properties of the CMC foliation. A useful discussion of these parameters can be found in [41].…”

“…Until now, numerical studies of the hyperboloidal initial value problem for test fields have been restricted to one or two dimensional codes [7][8][9][10][11][12][13][14] with the exception of [15]. The hyperboloidal approach has been shown to be accurate and efficient in lower dimensional studies, but in [15] the authors report large numerical errors in the simulation of Maxwell fields across future null infinity in flat spacetime with a 3D code based on Cartesian coordinates.…”

“…The hyperboloidal approach has been shown to be accurate and efficient in lower dimensional studies, but in [15] the authors report large numerical errors in the simulation of Maxwell fields across future null infinity in flat spacetime with a 3D code based on Cartesian coordinates. They deal with this problem by adding an artificial cosmological term to the background and by artificially tilting the light cones beyond null infinity to make grid boundaries spacelike.…”