Traces of quantum fuzziness on the black hole shadow and particle deflection in the multi-fractional theory of gravity

Abstract

In this paper, we investigate the properties of black holes within the framework of multi-fractional theories of gravity, focusing on the effects of q-derivatives and weighted derivatives. These modifications, which introduce scale-dependent spacetime geometries, alter black hole solutions in intriguing ways. Within these frameworks, we analyze two key observable phenomena - black hole shadows and particle deflection angle in the weak field limit - using both analytical techniques and observational data from the Event Horizon Telescope (EHT) for M87* and Sgr A*. The study from $q$-derivative formalism reveals that the multi-scale length ${\ell }_{\ast }$ influences the size of the black hole shadow in two ways, and modifies the weak deflection angle. Constraints on ${\ell }_{\ast }$ are derived from the EHT observations, showing significant deviations from standard Schwarzschild black hole predictions, which range from $10^9$ to $10^{10}$ orders of magnitude. Additionally, the weak deflection angle is computed using the non-asymptotic generalization of the Gauss-Bonnet theorem, revealing the effects of finite-distance and multi-scale parameters. Using the Sun for Solar System test, the constraints for ${\ell }_{\ast }$ range from $10^8$ to $10^9$ orders of magnitude. Results from the weighted derivative formalism generates a dS/AdS-like behavior, where smaller deviations are found in the strong field regime than in the weak field regime. The results suggest that while these effects are subtle, they provide a potential observational signature of quantum gravity effects. The findings presented here contribute to the broader effort of testing alternative theories of gravity through black hole observations, offering a new perspective on the quantum structure of spacetime at cosmological and astrophysical scales.

10 pages. Comments are welcome!

References in corpus (44)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Calculating black hole shadows: Review of analytical studies
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Relativistic images of Schwarzschild black hole lensing
• Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Constraints on black-hole charges with the 2017 EHT observations of M87*
• Shadow of five-dimensional rotating Myers-Perry black hole
• The innermost stable circular orbit and shadow in the novel $4D$ Einstein-Gauss-Bonnet gravity
• Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA
• Shadows and gravitational weak lensing by the Schwarzschild black hole in the string cloud background with quintessential field
• Image of Kerr-Melvin black hole with thin accretion disk
• QED Effect on Black Hole Shadow
• Distortions of images of Schwarzschild lensing
• Deflection Angle and Shadow Behaviors of Quintessential Black Holes in arbitrary Dimensions
• Circular orbit of a particle and weak gravitational lensing
• Cosmological constant corrections to the photon sphere and black hole shadow radii
• Shadows and lensing of black holes immersed in strong magnetic fields
• Shadow and quasinormal modes of the Kerr-Newman-Kiselev-Letelier black hole
• Quasiperiodic oscillations, weak field lensing and shadow cast around black holes in Symmergent gravity
• The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach
• White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era
• Motion of Particles and Gravitational Lensing Around (2+1)-dimensional BTZ black holes in Gauss-Bonnet Gravity
• Some Observable Physical Properties of the Higher Dimensional dS/AdS Black Holes in Einstein-Bumblebee Gravity Theory
• Constraints on charged Symmergent black hole from shadow and lensing
• Hunting extra dimensions in the shadow of Sgr A*
• Asymptotically locally flat and AdS higher-dimensional black holes of Einstein-Horndeski-Maxwell gravity in the light of EHT observations: shadow behavior and deflection angle
• Null geodesics, quasinormal modes and the correspondence with shadows in high-dimensional Einstein-Yang-Mills spacetimes
• Shadow of regular black hole in scalar-tensor-vector gravity theory
• How different are shadows of compact objects with and without horizons?
• Shadows of magnetically charged rotating black holes surrounded by quintessence
• Shadow of the $5D$ Reissner-Nordström AdS Black Hole
• High-dimensional Schwarzschild black holes in scalar-tensor-vector gravity theory
• Constraints from Solar System tests on a covariant loop quantum black hole
• Superentropic Black Hole Shadows in Arbitrary Dimensions
• Hunting for extra dimensions in black hole shadows
• Deflection and Gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit
• Analyzing the effect of higher dimensions on the black hole silhouette, deflection angles, and PINN approximated quasinormal modes
• Shadow of higher dimensional collapsing dark star and blackhole
• Asymptotically-Flat Black Hole Solutions in Symmergent Gravity

Cited by in corpus (2)

• Probing Quantum Gravity in Stellar Spacetimes: Phenomenological Insights
• Phenomenology of Schwarzschild-like Black Holes with a Generalized Compton Wavelength