Multi-probe analysis of strong-field effects in $f(Q)$ gravity

TL;DR

The paper tests covariant $f(Q)$ gravity in strong-field regimes by deriving static, spherically symmetric BH solutions for two symmetric-connection branches and confronting them with horizon-scale observables. Using photon-sphere and shadow analyses, Bozza strong-deflection lensing, and measurements from EHT for M87* and Sgr A*, along with S2-star precession, it shows Case I remains essentially GR-like while Case II can yield sizable deviations near the photon sphere, tightly constrained by current data. The multi-probe approach yields robust bounds on the deformation parameter $oldsymbol{α}$, with M87* providing the strongest constraints, particularly for the $n=2$ case, and demonstrates the power of horizon-scale imaging combined with precision astrometry to test nonmetricity-based gravity. The work outlines clear paths for future tests with next-generation horizon-scale imaging, ngEHT, and high-precision Galactic-center astrometry, enabling increasingly stringent scrutiny of $f(Q)$ models.

Abstract

Covariant $f(Q)$ gravity is a viable extension of General Relativity, however its strong-field predictions remain largely untested. Using the static, spherically symmetric black-hole solutions of the theory, we confront it with the most stringent probes available: black-hole shadows, Event Horizon Telescope (EHT) measurements, S2-star precession, and strong gravitational lensing. We show that the two admissible solution branches behave very differently: Case~I produces negligible deviations from Schwarzschild solution, whereas Case~II yields significant, potentially observable corrections to the photon sphere and shadow size. From the EHT shadow diameters of M87* and Sgr~A*, we obtain tight bounds, which are further strengthened by strong-lensing coefficients. These results provide the sharpest strong-field constraints on covariant $f(Q)$ gravity to date, and point toward future tests using next-generation horizon-scale imaging and precision Galactic-center astrometry.

Figures (4)

• Figure 1: The black hole shadow of Case II solution in the equatorial plane with $n=2$ (upper panel), and $n=3$ (lower panel) for fixed value of $\alpha=0.1$ in Planck mass units.
• Figure 2: A representative example of null geodesics in the equatorial plane of the Case II black-hole solution with $n=2$ and $\alpha=0.1$ in Planck mass units.
• Figure 3: The allowed range of $\alpha/M^2$ (upper panel), and $\alpha/M^4$ (lower panel) for Case II black-hole solution with $n=2, 3$ in light of EHT diameter measurement of M87*. The black-dashed line represents the central value of $R_s/M$ in EHT data, while the red-dashed lines mark the lower and upper permissible bounds.
• Figure 4: The allowed range of $\alpha/M^2$ (upper panel), and $\alpha/M^4$ (lower panel) for Case II black-hole solution with $n=2, 3$ in light of EHT diameter measurement of Sgr A*. The black-dashed line represents the central value of $R_s/M$ in EHT data, while the red-dashed lines mark the lower and upper permissible bounds.