Joint Constraints on Quantum Oppenheimer--Snyder Black Holes from High-Frequency Quasi-Periodic Oscillations in X-ray Binary Systems and the S2 Star Orbit

RESUMO

We study a quantum-corrected version of the Oppenheimer--Snyder (OS) spacetime in which classical collapse is modified by a single effective-parameter \(\alpha\), representing small-quantum-gravitational effects in a phenomenologically rescaled-form. Although the correction enters through a term proportional to \(\alpha M^2/r^4\), it produces noticeable changes in the strong-field region while leaving weak-field physics almost unchanged. One of the main results is the appearance of a minimum-mass for horizon-formation, \(M_{\min} \sim(0.5-1.2)\,M_\odot\) for the effective-parameter \(\alpha\approx0.22\). We emphasize that this \(M_{\min}\) is expressed in terms of the effective-parameter \(\alpha\); in terms of the bare loop-quantum-gravity (LQG) parameter, \(M_{\min}\sim M_{\text{Pl}}\sim10^{-5}\)~g, consistent with the theoretical-expectation. Orbital properties are also slightly modified, with the innermost-stable-circular-orbit (ISCO) shifting to \(r_{\rm ISCO}=6M-\alpha/(12M)\), giving corrections-of-order \( \sim 10^{-4} \) for stellar-black-holes and \(\sim 10^{-10}\) for Sgr A$^\ast$. In the same region, radial epicyclic frequencies change by about \(5\%-10\%\) near \(r\sim5M\), while vertical modes are less affected, leading to small but structured shifts in quasi-periodic oscillation (QPO) behavior. Using four X-ray binaries (GRS 1915+105, XTE J1550-564, XTE J1859+226, GRO J1655-40), we find a consistent range \(\alpha=0.22\pm0.10\), with masses between \(5.4-12.4\,M_\odot\) and emission radii \(r/M \sim 5.5 - 8.6\). The observed QPO frequencies, lying in the range \(100-450\) Hz, are well reproduced within this framework. Weak-field tests such as S2 and Mercury still allow \(f_{\rm sp}=1.10 \pm 0.19\), leaving room for these small strong-gravity corrections.