The properties and predictions of quasi-periodic oscillations around a black hole in nonlocal gravity

Abstract

We investigate the dynamics of massive test particles around a static black hole in nonlocal gravity and examine the corresponding properties of HF QPOs, constraining the nonlocal parameter to $\alpha/M \leq 0.452$. The nonlocal parameter $\alpha$ enhances the effective potential $V_{eff}$ and leads to a systematic reduction in the energy E and angular momentum L of circular orbits. Consequently, the ISCO radius, along with the associated energy and angular momentum, decreases monotonically with $\alpha$, while the radiative efficiency increases, reaching a maximum of approximately $8.9\%$. Due to the spherical symmetry of the spacetime, the Keplerian frequency $\Omega_{\phi}$ and the vertical epicyclic frequency $\Omega_{\theta}$ coincide and are suppressed by $\alpha$, whereas the radial epicyclic frequency $\Omega_{r}$ is enhanced. The impact of $\alpha$ on several twin-peak HF QPO models is examined, revealing that $\alpha$ increases both the lower and upper bounds of the predicted QPO frequency ranges. By imposing the $2\nu_U = 3\nu_L$ resonance condition, we analyze the resonant radius, upper QPO frequency, maximum allowed black hole mass, and the time delay between the shadow and QPO signals. We find that the resonant radius decreases with $\alpha$, while the upper QPO frequency increases, spanning the range $\nu_U \sim(673/M-4360/M)$Hz. When the TOV imit is imposed, the upper frequency is further constrained to $\nu_U \lesssim 1450$Hz. Combining astronomical observations for the classification of QPOs, where $\nu_U \geq 100$Hz, the black hole mass in the nonlocal gravity should satisfy $M \lesssim 43.6M_\odot$. Although the radial separation between the resonant radius and the photon sphere decreases with $\alpha$, the associated gravitational time delay increases, remaining below $\sim 1.3$ms and thus negligible for current observational capabilities.