Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System

TL;DR

This paper demonstrates the first successful evolution of the Einstein-Maxwell-Klein-Gordon system on hyperboloidal slices using standard formulations, enabling direct extraction of radiation signals at null infinity in spherical symmetry.

Contribution

It introduces a novel numerical approach for evolving coupled Einstein-Maxwell-Klein-Gordon equations on hyperboloidal slices with standard formulations like BSSN/Z4.

Findings

Simulated charged scalar field perturbations near black holes.

Successfully evolved collapse into Reissner-Nordström black holes.

Extracted radiation signals at null infinity.

Abstract

We present simulations of the Einstein-Maxwell-Klein-Gordon system on compactified hyperboloidal slices. To the best of our knowledge, this is the first time that this setup is evolved with a common formulation like BSSN/Z4. Hyperboloidal slices smoothly reach future null infinity, the only location in spacetime where radiation (such as gravitational waves) is unambiguously defined. We are thus able to reach null infinity and extract signals there. We showcase the capabilities of our implementation in spherical symmetry with the evolution of a charged scalar field perturbing a regular spacetime and near an electrically charged black hole. We also present the collapse of a charged scalar field into a Reissner-N\"ordstrom black hole.