Strong gravitational lensing in a rotating Kaluza-Klein black hole with squashed horizons

We have investigated the strong gravitational lensing in a rotating squashed Kaluza-Klein (KK) black hole spacetime. Our result show that the strong gravitational lensings in the rotating squashed KK black hole spacetime have some distinct behaviors from those in the backgrounds of the four-dimensional Kerr black hole and of the squashed KK Godel black hole. In the rotating squashed KK black hole spacetime, the marginally circular photon radius rho(ps), the coefficient (a) over bar, (b) over bar, the deflection angle alpha(theta) in the phi direction and the corresponding observational variables are independent of whether the photon goes with or against the rotation of the background, which is different with those in the usual four-dimensional Kerr black hole spacetime. Moreover, we also find that with the increase of the scale of extra dimension rho(0), the marginally circular photon radius rho(ps) and the angular position of the relativistic images theta infinity first decreases and then increases in the rotating squashed KK black hole for fixed rotation parameter b, but in the squashed KK Godel black hole they increase for the smaller global rotation parameter j and decrease for the larger one. In the extremely squashed case rho(0) = theta, the coefficient (a) over bar in the rotating squashed KK black hole increases monotonously with the rotation parameter, but in the squashed KK Godel black hole it is a constant and independent of the global rotation of the Godel Universe. These information could help us to understand further the effects of the rotation parameter and the scale of extra dimension on the strong gravitational lensing in the black hole spacetimes.