Gravitational lensing by a stable rotating regular black hole

Recent observational data from the Event Horizon Telescope (EHT) collaboration provide convincing realistic evidence for the existence of black hole rotation. From a phenomenological perspective, a recently proposed stable rotating regular (SRR) black hole circumvents the theoretical flaws of the Kerr solution. For the purpose of obtaining observational signatures of this black hole, we study its gravitational lensing effect. In the strong field limit, we calculate the deflection angle of light, the radius of the photon sphere, and other observables. The observables include the relativistic image position, separation, magnification, and time delays between different images. Then, by modeling M87* and Sgr A* as the SRR black hole, we compute their observables and evaluate the deviation of the observables from the Kerr case. In the weak field limit, we calculate the light deflection angle of M87* and Sgr A* via the Gauss-Bonnet theorem (GBT). With the growth of deviation parameter $e$, the gravitational lensing effect in the weak field limit intensifies monotonically, and the gravitational lensing effect in the strong field limit changes dramatically only at high spins. Our research may contribute to distinguish between SRR black holes from Kerr black holes under higher-precision astronomical observations.