Scalar decoupling and critical-curve invariance in a reduced MOG black-hole theory
Abstract
Linear perturbations of a Schwarzschild-MOG black hole separate into scalar and gravito-vector sectors in the reduced strong-field theory at leading order in μG̅ M≪1. The field redefinition ĥμν=hμν−ψg̅μν gives a decoupled Klein--Gordon equation for the scalar and the Reissner--Nordström equations for the gravito-vector sector. The scalar is stable under the stated spectral boundary conditions for mG2≥0. A scalar-only excitation produces a conformal metric perturbation with null Hamiltonian contribution H1(s)=−ψH0. For fixed observer worldlines and conformally corresponding orthonormal frames, every linear scalar-to-critical-curve transfer coefficient vanishes, including monopole breathing, provided the conformal factor is smooth, positive, and preserves the capture boundary. The exceptional charged axial dipole instead induces a constrained metric perturbation. A first-order radial integral reconstructs this perturbation in a gauge regular at the future horizon and on the sphere, separating the radiative amplitude from stationary angular momentum without division by frequency. For a unit-incident canonical vector amplitude with zero angular momentum, matched asymptotic solutions give an explicit charge-dependent local metric response that vanishes as ω2 at fixed radius and fixed subextremal background. A separate infinitesimal Kerr--Newman benchmark yields the stationary impact-parameter midpoint shift and recovers δCb=−2arot in the neutral limit. These results exclude linear scalar breathing of the specified angular critical curve and distinguish the low-frequency vector-induced metric response from a stationary rotation effect.
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BibTeX
@misc{lobos2026scalar,
title = {{Scalar decoupling and critical-curve invariance in a reduced MOG black-hole theory}},
author = {Nikko John Leo S. Lobos and Emmanuel T. Rodulfo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03751},
eprint = {2610.03751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03751},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scalar decoupling and critical-curve invariance in a reduced MOG black-hole theory
AU - Nikko John Leo S. Lobos
AU - Emmanuel T. Rodulfo
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03751
UR - https://arxiv.org/abs/2610.03751
AB - Linear perturbations of a Schwarzschild-MOG black hole separate into scalar and gravito-vector sectors in the reduced strong-field theory at leading order in μG̅ M≪1. The field redefinition ĥ_μν=h_μν−ψg̅_μν gives a decoupled Klein--Gordon equation for the scalar and the Reissner--Nordström equations for the gravito-vector sector. The scalar is stable under the stated spectral boundary conditions for m_G^2≥0. A scalar-only excitation produces a conformal metric perturbation with null Hamiltonian contribution H_1^(s)=−ψH_0. For fixed observer worldlines and conformally corresponding orthonormal frames, every linear scalar-to-critical-curve transfer coefficient vanishes, including monopole breathing, provided the conformal factor is smooth, positive, and preserves the capture boundary. The exceptional charged axial dipole instead induces a constrained metric perturbation. A first-order radial integral reconstructs this perturbation in a gauge regular at the future horizon and on the sphere, separating the radiative amplitude from stationary angular momentum without division by frequency. For a unit-incident canonical vector amplitude with zero angular momentum, matched asymptotic solutions give an explicit charge-dependent local metric response that vanishes as ω^2 at fixed radius and fixed subextremal background. A separate infinitesimal Kerr--Newman benchmark yields the stationary impact-parameter midpoint shift and recovers δC_b=−2a_rot in the neutral limit. These results exclude linear scalar breathing of the specified angular critical curve and distinguish the low-frequency vector-induced metric response from a stationary rotation effect.
ER -