Non-minimally coupled Weyl connection gravity in the Solar System and at the Galactic Center
7 affiliations
- 1Institute for Research in Fundamental Sciences (IPM)
- 2Damghan University
- 3Khazar University
- 4Universidade de Lisboa
- 5Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Universidade de Lisboa
- 6Universidade dos Açores
- 7Centro de Física das Universidades do Minho e do Porto
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 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 ω using current observational data. For Solution I (purely radial Weyl vector), the leading metric corrections scale as 1/ω 1 / ω , yielding bounds as strong as ω > rsim 1030 ω ≳ 10 30 m from perihelion precession. For Solution II (time-radial Weyl vector), the corrections scale as 1/ω 2 1 / ω 2 , resulting in weaker constraints, with ω > rsim 1020 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 2 r / ω that dominates in the Solar System regime, Solution II features a linear term suppressed by an additional factor of M/ω M / ω , making the quadratic term −r2/4ω 2 - r 2 / 4 ω 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. For Solution I, the S2 periastron precession yields ω > rsim 1021 ω ≳ 10 21 m, while the S2 gravitational redshift provides the stronger constraint ω > rsim 1024 ω ≳ 10 24 m. For Solution II, the corresponding bounds are ω > rsim 1017 ω ≳ 10 17 m from periastron precession and ω > rsim 1022 ω ≳ 10 22 m from gravitational redshift. While Solar System tests probe the weak-field regime, these stellar-orbit observations extend the analysis to a substantially stronger gravitational environment. The stellar-orbit analysis reveals a qualitative distinction: Solution I produces a retrograde correction to the periastron precession, while Solution II produces a prograde one, mirroring the behavior identified in the Solar System. Finally, despite both solutions sharing the same quadratic asymptotic structure, only Solution II can accommodate an effective cosmological constant of the same order as the observed value, Λ obs ∼ 10−52 Λ obs ∼ 10 - 52 m −2 - 2 , while Solution I is constrained to produce a negligibly small effective Λ Λ .
Versions
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BibTeX
@article{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},
journal = {The European Physical Journal C},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16513-2},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16513-2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
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 - 2026/10/26
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16513-2
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16513-2
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 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 ω using current observational data. For Solution I (purely radial Weyl vector), the leading metric corrections scale as 1/ω 1 / ω , yielding bounds as strong as ω > rsim 10^30 ω ≳ 10 30 m from perihelion precession. For Solution II (time-radial Weyl vector), the corrections scale as 1/ω ^2 1 / ω 2 , resulting in weaker constraints, with ω > rsim 10^20 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 2 r / ω that dominates in the Solar System regime, Solution II features a linear term suppressed by an additional factor of M/ω M / ω , making the quadratic term −r^2/4ω ^2 - r 2 / 4 ω 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. For Solution I, the S2 periastron precession yields ω > rsim 10^21 ω ≳ 10 21 m, while the S2 gravitational redshift provides the stronger constraint ω > rsim 10^24 ω ≳ 10 24 m. For Solution II, the corresponding bounds are ω > rsim 10^17 ω ≳ 10 17 m from periastron precession and ω > rsim 10^22 ω ≳ 10 22 m from gravitational redshift. While Solar System tests probe the weak-field regime, these stellar-orbit observations extend the analysis to a substantially stronger gravitational environment. The stellar-orbit analysis reveals a qualitative distinction: Solution I produces a retrograde correction to the periastron precession, while Solution II produces a prograde one, mirroring the behavior identified in the Solar System. Finally, despite both solutions sharing the same quadratic asymptotic structure, only Solution II can accommodate an effective cosmological constant of the same order as the observed value, Λ _obs ∼ 10^−52 Λ obs ∼ 10 - 52 m ^−2 - 2 , while Solution I is constrained to produce a negligibly small effective Λ Λ .
SN - 1434-6044
SN - 1434-6052
ER -