Nonlinear completions of the Ricci coupling in black-hole scalarization
Abstract
We study spontaneous scalarization of static, spherically symmetric black holes in scalar--Gauss--Bonnet gravity with a Ricci coupling F=1 βϕ2/4+γβ2ϕ4+O(ϕ6) that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in β, changes sign at β=1.1156, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to γ. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as γ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.
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BibTeX
@misc{parida2026nonlinear,
title = {{Nonlinear completions of the Ricci coupling in black-hole scalarization}},
author = {Subrat Parida},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03779},
eprint = {2610.03779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03779},
}
RIS
TY - UNPB
TI - Nonlinear completions of the Ricci coupling in black-hole scalarization
AU - Subrat Parida
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03779
UR - https://arxiv.org/abs/2610.03779
AB - We study spontaneous scalarization of static, spherically symmetric black holes in scalar--Gauss--Bonnet gravity with a Ricci coupling F=1 βϕ^2/4+γβ^2ϕ^4+O(ϕ^6) that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in β, changes sign at β=1.1156, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to γ. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as γ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.
ER -