Shadows of rotating Hayward–de Sitter black holes with astrometric observables

Motivated by recent work on rotating black hole shadow (Chang and Zhu in Phys Rev D 101:084029, 2020), we investigate the shadow behaviours of rotating Hayward–de Sitter black hole for static observers at a finite distance in terms of astronomical observables. This paper uses the newly introduced distortion parameter (Chang and Zhu in Phys Rev D 102:044012, 2020) to describe the shadow’s shape quantitatively. We show that the spin parameter would distort shadows and the magnetic monopole charge would increase the degree of deformation. The distortion will increase as the distance between the observer and the black hole increases, and distortion reduces as the cosmological constant increases. Besides, the increase of the spin parameter, magnetic monopole charge and cosmological constant will cause the shadows shrunken.

Black hole shadow with a cosmological constant for cosmological observers

We investigate the effect of the cosmological constant on the angular size of a black hole shadow. It is known that the accelerated expansion which is created by the cosmological constant changes the angular size of the black hole shadow for static observers. However, the shadow size must be calculated for the appropriate cosmological observes. We calculate the angular size of the shadow measured by cosmological comoving observers by projecting the shadow angle to this observer rest frame. We show that the shadow size tends to zero as the observer approaches the cosmological horizon. We estimate the angular size of the shadow for a typical supermassive black hole, e.g M87. It is found that the angular size of the shadow for cosmological observers and static observers is approximately the same at these scales of mass and distance. We present a catalog of supermassive black holes and calculate the effect of the cosmological constant on their shadow size and find that the effect could be $$3\ precent$$3precent for distant sources.