Constraining Ho\v{r}ava-Lifshitz gravity by weak and strong gravitational lensing

Abstract

We discuss gravitational lensing in the Kehagias-Sfetsos space-time emerging in the framework of Ho\v{r}ava-Lifshitz gravity. In weak lensing we show that there are three regimes, depending on the value of $\bar {\lambda}=1/\omega d^{2}$, where $\omega $ is the Ho\v{r}ava-Lifshitz parameter and $d$ characterizes the lensing geometry. When $\bar {\lambda}$ is close to zero, light deflection typically produces two images, as in Schwarzschild lensing. For very large $\bar {\lambda}$ the space-time approaches flatness, therefore there is only one undeflected image. In the intermediate range of $\bar {\lambda}$ only the upper focused image is produced due to the existence of a maximal deflection angle $\delta_{max}$, a feature inexistent in the Schwarzschild weak lensing. We also discuss the location of Einstein rings, and determine the range of the Ho\v{r}ava-Lifshitz parameter compatible with present day lensing observations. Finally, we analyze in the strong lensing regime the first two relativistic Einstein rings and determine the constraints on the parameter range to be imposed by forthcoming experiments.