We investigate covariant loop quantum black hole models in effective quantum gravity by using the orbital motion of the S2 star around Sagittarius ${\mathrm{A}}^{\star }$. Three representative covariant metrics that preserve general covariance while incorporating distinct quantum corrections are analyzed: two derived with relaxed gauge-fixing conditions and one nonsingular model with holonomy corrections. By investigating orbital motions from the geodesic equations and comparing with astrometric and spectroscopic observations from the GRAVITY Collaboration, we perform a Markov chain Monte Carlo analysis to search for loop quantum gravity signatures. No statistically significant evidence for quantum modifications is found. The 95% credible upper limits on the dimensionless deformation parameter are $\zeta \lesssim 0.723$ for model I, $\zeta \lesssim 88.622$ for model II, while no meaningful constraint can be placed on model III with the current data. A complementary analysis within the parametrized post-Newtonian framework likewise reveals no detectable deviations from general relativity. Such results imply that current data of the S2 star possess less ability of searching the signal beyond general relativity within the spherically symmetric spacetimes.

Close

PrevNext

View figure in article

• Alternative gravity theories