Rotating regular black holes in conformal massive gravity

In this paper, we use a suitable conformal rescaling to construct static and rotating regular black holes in conformal massive gravity. The new metric is characterized by the mass $M$, the "scalar charge" $Q$, the angular momentum parameter $a$, the "hair parameter" $\lambda$, and the conformal scale factor encoded in the parameter $L$. We explore the shadow images and the deflection angles of relativistic massive particles in the spacetime geometry of a rotating regular black hole. For $\lambda \neq 0$ and $Q > 0$, the shadow is larger than the shadow of a Kerr black hole. In particular, if $\lambda < 0$, the shadow radius increases considerably. For $\lambda \neq 0$ and $Q < 0$, the shadow is smaller than the shadow of a Kerr black hole. Additionally we put observational constraints on the parameter $Q$ using the latest Event Horizon Telescope (EHT) observation of the supermassive black hole M87*. Lastly, using the Gauss-Bonnet theorem, we show that the deflection angle of massive particles is strongly affected by the parameter $L$. The deflection angle might be used to distinguish rotating regular black holes from rotating singular black holes.