Strong gravitational lensing of a five-dimensional charged, equally rotating black hole with a cosmological constant

Abstract: We study the lensing phenomena of the strong gravity regime of five-dimensional charged, equally rotating black holes with a cosmological constant, familiarly known as the Cveti\v c-L\"u-Pope black holes. These black holes are characterized by three observable parameters, the mass $M$, the charge $Q$ and the angular momentum $J$, in addition to the cosmological constant. We investigate the strong gravitational lensing observables, mainly the photon sphere radius, the minimum impact parameter, the deflection angle, the angular size, and the magnification of the relativistic images. We model the $M87$ and $SgrA^*$ for these observables. We also focus on the relativistic time delay effect in the strong-field regime of gravity and the impact of the observable on it. The analytical expressions for the observables of the relativistic images with vanishing angular momentum ($j=0$) are discussed in some detail. We shed a light on the gravitational time delay effect by incorporating the lensing observables. The gravitational time delay has a direct consequence on the photon sphere radius and hence on the quasinormal modes.