Comment on "Charged scalar field at future null infinity via nonlinear hyperboloidal evolution" [Phys. Rev. D {\bf 112}, 104053 (2025), arXiv:2506.15311]

TL;DR

This paper critiques recent numerical findings on late-time tails of charged scalar fields, clarifying inaccuracies and emphasizing the importance of correct analysis in understanding black hole physics.

Contribution

It identifies and corrects errors in recent numerical studies of charged scalar field tails, reaffirming earlier analytical and numerical results from three decades ago.

Findings

Discrepancies in recent numerical results highlighted

Errors in analysis and claims of AVV addressed

Reaffirmation of Hod and Piran's original findings

Abstract

The asymptotically decaying tails that characterize the late-time dynamics of collapsing self-gravitating charged massless scalar fields were studied three decades ago by Hod and Piran (HP). In particular, it was shown, both analytically and numerically, that the late-time behavior of these collapsing charged massless scalar fields is governed by oscillatory inverse power law tails, which decay more slowly than the familiar tails of neutral massless fields. Recently \'Alvares and Va\~no-Vi\~nuales (AVV) have investigated the same model numerically. While most of their results are in very good agreement with the earlier findings of HP, there are also some discrepancies between the original results of HP and those reported by AVV. In this compact comment, we wish to highlight a number of inaccurate claims and critical errors in the analysis and results presented by AVV.