Weakly nonlinear strong-field signatures of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes near the Schwarzschild bifurcation
Abstract
We study the static, spherically symmetric electric branch of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes close to its Schwarzschild bifurcation. A weakly nonlinear expansion is built around the fundamental vector zero mode. The critical coupling is determined independently by shooting and collocation, the second-order metric correction is checked against the unreduced covariant equations, and the corresponding ADM-mass correction is shown to vanish analytically. The leading departure of the vectorized branch from the bifurcation point follows from a third-order Fredholm solvability condition. Using the resulting metric, we calculate the leading corrections to the photon sphere, shadow scale, marginally bound orbit, innermost stable circular orbit, orbital and epicyclic frequencies, the geometric three-to-two frequency-ratio radius, the instability of the circular photon orbit, and the logarithmic strong-deflection coefficient. Near the bifurcation, the photon sphere and innermost stable orbit move outward, whereas the three-to-two radius moves inward. The photon-orbit angular frequency decreases and its Lyapunov exponent increases. These results characterize the local strong-field geometry of the electric vectorized branch. They are not intended as observational constraints or as an extrapolation to the strongly nonlinear regime.
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BibTeX
@misc{murodov2026weakly,
title = {{Weakly nonlinear strong-field signatures of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes near the Schwarzschild bifurcation}},
author = {Sardor Murodov and Bekzod Rahmatov and Islom Egamberdiev and Dilnavoz Kamalova and Javlon Rayimbaev and Bobomurat Ahmedov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26266},
eprint = {2609.26266},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26266},
}
RIS
TY - UNPB
TI - Weakly nonlinear strong-field signatures of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes near the Schwarzschild bifurcation
AU - Sardor Murodov
AU - Bekzod Rahmatov
AU - Islom Egamberdiev
AU - Dilnavoz Kamalova
AU - Javlon Rayimbaev
AU - Bobomurat Ahmedov
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26266
UR - https://arxiv.org/abs/2609.26266
AB - We study the static, spherically symmetric electric branch of spontaneously vectorized Einstein-vector-Gauss-Bonnet black holes close to its Schwarzschild bifurcation. A weakly nonlinear expansion is built around the fundamental vector zero mode. The critical coupling is determined independently by shooting and collocation, the second-order metric correction is checked against the unreduced covariant equations, and the corresponding ADM-mass correction is shown to vanish analytically. The leading departure of the vectorized branch from the bifurcation point follows from a third-order Fredholm solvability condition. Using the resulting metric, we calculate the leading corrections to the photon sphere, shadow scale, marginally bound orbit, innermost stable circular orbit, orbital and epicyclic frequencies, the geometric three-to-two frequency-ratio radius, the instability of the circular photon orbit, and the logarithmic strong-deflection coefficient. Near the bifurcation, the photon sphere and innermost stable orbit move outward, whereas the three-to-two radius moves inward. The photon-orbit angular frequency decreases and its Lyapunov exponent increases. These results characterize the local strong-field geometry of the electric vectorized branch. They are not intended as observational constraints or as an extrapolation to the strongly nonlinear regime.
ER -