https://doi.org/10.1140/epjc/s10052-025-15228-0
Regular Article - Theoretical Physics
Fractal temporal dynamics in black hole accretion and quasi-periodic oscillation scaling
Department of Physics, Faculty of Science, Istanbul University, 34134, Istanbul, Turkey
a
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Received:
13
October
2025
Accepted:
14
December
2025
Published online:
28
December
2025
Abstract
Accretion processes around black holes play a central role in high-energy astrophysics by governing compact object growth and driving luminous emissions across the electromagnetic spectrum. In this work, we propose a theoretical framework in which the local flow of time near the event horizon acquires a fractal structure, potentially arising from quantum gravitational fluctuations at Planckian length scales. This fractal temporal behavior, characterized by a scaling relation 
with 
, modifies the time evolution of surface density in viscous accretion disks. We derive a generalized diffusion equation incorporating the fractal-time exponent 
and perform numerical simulations across a wide range of black-hole masses (
to 
) and accretion rates (0.01–
). Our results reveal enhanced modulation in the accretion luminosity and the emergence of quasi-periodic oscillations (QPOs) in the X-ray light curves. The predicted QPO frequencies, which range from 4–
for stellar-mass black holes, scale with the fractal exponent and follow 
(classical limit 
), remaining within the detection capabilities of current instruments such as NICER, XMM-Newton, and NuSTAR. These findings indicate that microscopic spacetime fluctuations may leave macroscopic imprints on accretion dynamics, thereby providing an observational probe of fractal-time behavior near black holes. This work offers a testable connection between quantum gravitational microphysics and observable X-ray variability.
© The Author(s) 2025
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