Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems

TL;DR

This paper presents a hybrid numerical method combining Cauchy and characteristic evolutions to simulate the Einstein-Klein-Gordon system with spherical symmetry, ensuring smooth data matching and high accuracy across the entire domain.

Contribution

It introduces a novel Cauchy-characteristic matching approach for Einstein-Klein-Gordon systems, improving accuracy and stability in spherical symmetry simulations.

Findings

Method achieves high accuracy across all M/R ranges.

Smooth matching conditions ensure consistent evolution.

Validated against reference solutions with excellent agreement.

Abstract

A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The matching interface between the space-like and characteristic foliations is constructed by imposing continuity conditions on metric, extrinsic curvature and scalar field variables, ensuring smoothness across the matching surface. The accuracy of the method is established for all ranges of $M/R$, most notably, with a detailed comparison of invariant observables against reference solutions obtained with a calibrated, global, null algorithm.