Non-minimally coupled Weyl connection gravity in the Solar System and at the Galactic Center
Abstract
We explore the phenomenological viability of non-minimally coupled Weyl connection gravity by confronting its static, spherically symmetric black hole solutions with classical weak-field Solar System tests and stellar-orbit observations near Sgr A*. In this geometric framework, non-metricity is encoded via a Weyl vector field, giving rise to two distinct families of Schwarzschild-like vacuum solutions characterized by a free parameter ω with dimensions of length. We compute the corrections to four classical observables---gravitational redshift, Mercury's perihelion advance, light deflection, and radar echo delay---and derive stringent lower bounds on ω using current observational data. For Solution I (purely radial Weyl vector), the leading metric corrections scale as 1/ω, yielding bounds as strong as ω≳ 1030 m from perihelion precession. For Solution II (time-radial Weyl vector), the corrections scale as 1/ω2, resulting in weaker constraints, with ω≳ 1020 m from the same test. This marked difference arises from the distinct behavior of the linear corrections in each solution: while Solution I exhibits an unsuppressed linear term 2r/ω that dominates in the Solar System regime, Solution II features a linear term suppressed by an additional factor of M/ω, making the quadratic term −r2/4ω2 dominant throughout. We then analyze stellar orbits near the Galactic Center, finding that current observations of the S2 star provide complementary constraints on both solutions. (...)
Versions
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BibTeX
@misc{khodadi2026nonminimally,
title = {{Non-minimally coupled Weyl connection gravity in the Solar System and at the Galactic Center}},
author = {Mohsen Khodadi and Margarida Lima and Cláudio Gomes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.24491},
eprint = {2608.24491},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24491},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-minimally coupled Weyl connection gravity in the Solar System and at the Galactic Center
AU - Mohsen Khodadi
AU - Margarida Lima
AU - Cláudio Gomes
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2608.24491
UR - https://arxiv.org/abs/2608.24491
AB - We explore the phenomenological viability of non-minimally coupled Weyl connection gravity by confronting its static, spherically symmetric black hole solutions with classical weak-field Solar System tests and stellar-orbit observations near Sgr A*. In this geometric framework, non-metricity is encoded via a Weyl vector field, giving rise to two distinct families of Schwarzschild-like vacuum solutions characterized by a free parameter ω with dimensions of length. We compute the corrections to four classical observables---gravitational redshift, Mercury's perihelion advance, light deflection, and radar echo delay---and derive stringent lower bounds on ω using current observational data. For Solution I (purely radial Weyl vector), the leading metric corrections scale as 1/ω, yielding bounds as strong as ω≳ 10^30 m from perihelion precession. For Solution II (time-radial Weyl vector), the corrections scale as 1/ω^2, resulting in weaker constraints, with ω≳ 10^20 m from the same test. This marked difference arises from the distinct behavior of the linear corrections in each solution: while Solution I exhibits an unsuppressed linear term 2r/ω that dominates in the Solar System regime, Solution II features a linear term suppressed by an additional factor of M/ω, making the quadratic term −r^2/4ω^2 dominant throughout. We then analyze stellar orbits near the Galactic Center, finding that current observations of the S2 star provide complementary constraints on both solutions. (...)
ER -