Charged Scalar Field at Future Null Infinity via Nonlinear Hyperboloidal Evolution

TL;DR

This paper employs nonlinear hyperboloidal evolution to analyze charged scalar fields at future null infinity, providing independent verification of quasinormal modes and decay tails consistent with previous studies, using full non-linear evolutions.

Contribution

It introduces a hyperboloidal formalism approach to study charged scalar fields at null infinity, offering an independent comparison to prior non-linear results and confirming previous findings.

Findings

Good agreement with prior prescriptions for oscillation frequencies

Accurate modeling of power-law decay tails

Successful extraction of signals at future null infinity

Abstract

Quasinormal modes and power-law late-time decay tails of a charged scalar field on a charged black hole have been considered in the literature, and here we use the hyperboloidal formalism to present an independent comparison to prior non-linear results. For the quasinormal modes we show a fit of the spherical fundamental mode for the purely uncharged case and compare it to the charged one. We obtain good agreement with prior prescriptions for the oscillation frequency between real and imaginary parts of the scalar field, as well as for the exponent of the power-law decay. Full non-linear evolutions of hyperboloidal slices in spherical symmetry were used to obtain our results, allowing for the extraction of signals at future null infinity.