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 high-frequency quasi-periodic oscillations (HF QPOs), constraining the nonlocal parameter to $$\alpha /M \le 0.452$$ α / M ≤ 0.452 . We show that the nonlocal parameter $$\alpha $$ α enhances the effective potential $$V_{\text {eff}}$$ V eff and leads to a systematic reduction in the energy $$\mathcal {E}$$ E and angular momentum $$\mathcal {L}$$ L of circular orbits. Consequently, the innermost stable circular orbit (ISCO) radius, along with the associated energy and angular momentum, decreases monotonically with $$\alpha $$ α , while the radiative efficiency increases, reaching a maximum of approximately $$8.9\%$$ 8.9 % . We further analyze the fundamental orbital frequencies of test particles and find that, due to the spherical symmetry of the spacetime, the Keplerian frequency $$\Omega _{\phi }$$ Ω ϕ and the vertical epicyclic frequency $$\Omega _{\theta }$$ Ω θ coincide and are suppressed by $$\alpha $$ α , whereas the radial epicyclic frequency $$\Omega _{r}$$ Ω r is enhanced. The impact of $$\alpha $$ α on several twin-peak HF QPO models is examined, revealing that $$\alpha $$ α increases both the lower and upper bounds of the predicted QPO frequency ranges. By imposing the $$2\nu _U = 3\nu _L$$ 2 ν U = 3 ν 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 $$\alpha $$ α , while the upper QPO frequency increases, spanning the range $$\nu _U \sim (673/M$$ ν U ∼ ( 673 / M