Shadow of quantum extended Kruskal black hole and its super-radiance property

Abstract

We perform the shadow calculation of the loop quantum gravity motivated regular black hole recently proposed by Ashtekar, Olmedo and Singh (will be termed AOS black hole hereafter). In the process, we also construct the rotating loop quantum gravity inspired solution of the originally proposed static spherically symmetric AOS black hole by applying the modified Newman-Janis algorithm. We study the quantum effects on the shadows of both the non-rotating and rotating loop quantum black hole solutions. It is observed that the general shape of the shadow for non-rotating AOS black hole is circular in shape as is expected for its classical counter part too, but the presence of loop quantum gravity inspired modification contracts the shadow radius and the effect reduces with the increase in the mass of the black hole. On a similar note, in the rotating situation, we find contraction in shadow radius due to quantum effects and the tapered nature of the shadow as expected from the classical Kerr case. However, instead of the symmetrical contraction, like non-rotating one, we found more contraction on one side relative to the other when we compare our result with the shadow of the Kerr black hole. We finally studied super-radiance in rotating AOS background and observed that the super-radiance condition for massless scalar field is identical to that of the Kerr case with the rotation of the BH being more compared to Kerr in the low mass regime. With an increase in mass of the rotating AOS black hole, the difference from Kerr starts to become insignificant.