# Shadow and deflection angle of rotating black hole in asymptotically safe gravity

## TL;DR

This paper analytically studies the shadows of rotating black holes in asymptotically safe gravity, revealing how ASG parameters influence shadow shape, size, and light deflection, and providing observational bounds on these parameters.

## Contribution

It derives complete null geodesics and shadow observables for rotating black holes in ASG, extending Kerr results and constraining ASG parameters using shadow data.

## Key findings

- Shadow size decreases with increasing ASG parameters.
- Shadow distortion increases with ASG parameters.
- Deflection angle modifications are of order microarcseconds.

## Abstract

We analytically investigate the shadows cast by rotating black holes in the asymptotically safe gravity (ASG) by deriving complete null geodesics and observables using the Hamilton-Jacobi equation and Carter separable method. It turns out that the apparent shape and size of the shadow depend on the ASG parameters ($\zeta, \gamma$) in addition to other black hole parameters ($M, a$). The size of black hole shadows monotonically decreases and shadows get more distorted with increasing values of ASG parameters when compared with the Kerr black hole shadows. In turn, we use shadow observables to estimate black hole spin and ASG parameters. Noteworthy, we find that the deflection angle of the light has been modified by ASG parameters to generalize the Kerr deflection angle, and the corrections in the deflection angle are of $\mathcal{O}(\mu$as). In the vanishing limits of ASG parameters, our results smoothly reduced to the Kerr black holes. The inferred circularity deviation $\Delta C\leq 0.10$ for the M87* black hole shadow merely constrains the ASG parameter $\zeta$, however, shadow angular diameter $\theta_d=42\pm 3\, \mu$as, within the $1\sigma$ region, places bounds $\zeta\leq 0.1324$ for $\gamma=0.10$.