Massive Scalar Quasinormal Modes and Quasibound States of Charged Black Holes with Logarithmic corrections
Abstract
We study how long-range deformations in a black-hole metric affect the oscillation, trapping, and decay of a neutral, minimally coupled massive scalar field. We choose a logarithmic deformation of Reissner-Nordström (RN) sourced by nonlinear electrodynamics. It provides an exact solution of Einstein gravity and admits a finite completion. The same geometry also arises in a phenomenological perfect-fluid dark-matter model. In this setup, we analyze both quasinormal modes (QNMs), which describe relaxation, and quasibound states (QBSs), which describe trapped modes with small horizon absorption. We first show that a small scalar mass moves the potential barrier outward, raises it, and reduces its curvature. First-order WKB then predicts weaker damping at every fixed finite multipole and overtone. We then compare several approaches, namely sixth-order WKB, global matching, a generalized Leaver method (adapted to the logarithmic geometry) and time-domain evolution. All methods yield consistent QNM estimates within their ranges of validity. Global matching and Leaver also agree closely for QBSs. Further analytic estimates with a reference trapped state show that a local Padé approximation gives a binding-energy error of about 0.04%, while leading Gamow tunnelling underestimates damping by about 25%. Across the sampled QBSs, increasing the scalar mass or nonlinear coupling strengthens binding but shortens the lifetime through greater horizon absorption. Finally, using an appropriate horizon regularization and a common complex radial contour, we demonstrate orthogonality of an independently computed QNM-QBS pair using a suitable relativistic bilinear framework.
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BibTeX
@misc{paul2026massive,
title = {{Massive Scalar Quasinormal Modes and Quasibound States of Charged Black Holes with Logarithmic corrections}},
author = {Prosenjit Paul and Rickmoy Samanta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33883},
eprint = {2610.33883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33883},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Massive Scalar Quasinormal Modes and Quasibound States of Charged Black Holes with Logarithmic corrections
AU - Prosenjit Paul
AU - Rickmoy Samanta
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33883
UR - https://arxiv.org/abs/2610.33883
AB - We study how long-range deformations in a black-hole metric affect the oscillation, trapping, and decay of a neutral, minimally coupled massive scalar field. We choose a logarithmic deformation of Reissner-Nordström (RN) sourced by nonlinear electrodynamics. It provides an exact solution of Einstein gravity and admits a finite completion. The same geometry also arises in a phenomenological perfect-fluid dark-matter model. In this setup, we analyze both quasinormal modes (QNMs), which describe relaxation, and quasibound states (QBSs), which describe trapped modes with small horizon absorption. We first show that a small scalar mass moves the potential barrier outward, raises it, and reduces its curvature. First-order WKB then predicts weaker damping at every fixed finite multipole and overtone. We then compare several approaches, namely sixth-order WKB, global matching, a generalized Leaver method (adapted to the logarithmic geometry) and time-domain evolution. All methods yield consistent QNM estimates within their ranges of validity. Global matching and Leaver also agree closely for QBSs. Further analytic estimates with a reference trapped state show that a local Padé approximation gives a binding-energy error of about 0.04%, while leading Gamow tunnelling underestimates damping by about 25%. Across the sampled QBSs, increasing the scalar mass or nonlinear coupling strengthens binding but shortens the lifetime through greater horizon absorption. Finally, using an appropriate horizon regularization and a common complex radial contour, we demonstrate orthogonality of an independently computed QNM-QBS pair using a suitable relativistic bilinear framework.
ER -