A fast stroboscopic spectral method for rotating systems in numerical relativity

TL;DR

This paper introduces a rapid spectral matching method for solving wave equations in rotating astrophysical systems, effectively avoiding light cylinder issues in numerical relativity.

Contribution

It develops a fast spectral matching technique between rotating and inertial domains, adaptable to various numerical schemes for simulating rotating compact objects.

Findings

Efficient spectral matching reduces computational complexity.

Method successfully handles rotating systems inside the light cylinder.

Applicable to different numerical schemes for evolution equations.

Abstract

We present a numerical technique for solving evolution equations, as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The technique implements a fast spectral matching between two domains in relative rotation: an inner spherical domain, comoving with the sources and lying strictly inside the light cylinder, and an outer inertial spherical shell. Even though the emphasis is placed on spectral techniques, the matching is independent of the specific manner in which equations are solved inside each domain, and can be adapted to different schemes. We illustrate the strategy with some simple but representative examples.