Black hole quasinormal modes, greybody factors, sparsity of Hawking radiation and quasi-periodic oscillations in a tetrad-frame Deser–Woodard nonlocal gravity

We investigate a wide range of dynamical and observational signatures of spherically symmetric static black holes in the non-local Deser-Woodard gravity model, distinguished by a non-local parameter α and an integer model order n. Starting from the modified metric functions, we derive the Klein–Gordon equation for a massless scalar field and transform it into a Schrödinger-like form using tortoise coordinates. We then compute the spectra of quasinormal modes (QNMs) employing both the sixth-order WKB approximation and its Padé-improved variants. We demonstrate that nonlocality systematically reduces the real frequencies of QNMs and increases damping. Additionally, we observe that the errors associated with the WKB approximation grow rapidly; however, the Padé method effectively reduces these errors to sub-percent levels. Next, we establish rigorous analytic lower bounds on greybody factors (GBFs) using the Visser–Boonserm method. This analysis demonstrates that an increase in either the parameter α or the integer model order n serves to elevate and expand the effective potential barrier, which in turn suppresses transmission at mid-frequency ranges. We quantified the sparsity of Hawking radiation by calculating the dimensionless sparsity parameter, η. Our findings indicate that nonlocal coupling, denoted by α, significantly reduces the value of η, which in turn accelerates the evaporation process. In contrast, higher values of n produce subtler effects. Notably, in all scenarios, we observe that η approaches ηSch as the horizon radius increases. Finally, we analyse the epicyclic (radial and vertical) oscillation frequencies of near-circular orbits, presenting them in a closed form and discussing their potential as probes for nonlocal corrections in quasi-periodic oscillations of accretion discs. Our findings underscore distinct, observationally testable signatures of nonlocal gravity on black hole spectroscopy, greybody emission, and the dynamics of accretion discs.