The 3-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

TL;DR

This paper extends a 3D characteristic numerical relativity code to include a massless scalar field, enabling accurate simulation of scalar and gravitational radiation from black hole interactions, with results matching theoretical predictions.

Contribution

It introduces a second-order convergent 3D code for the Einstein-Klein-Gordon system, allowing detailed simulations of scalar and gravitational radiation in black hole spacetimes.

Findings

Accurate calculation of gravitational and scalar radiation at infinity.

Scalar and gravitational radiation modes follow predicted power law scaling.

Final ring down matches perturbative quasinormal mode frequencies.

Abstract

We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein--Klein--Gordon system is calibrated to be second order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the $\ell=2$ quasinormal mode.