Particle motion around black hole in Hořava-Lifshitz gravity
Abstract
Analytical solutions of Maxwell equations around a black hole immersed in an external uniform magnetic field in the background of the Kehagias-Sfetsos (KS) asymptotically flat black hole solution of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity have been found. The influence of a magnetic field on the effective potential of the radial motion of a charged test particle around a black hole immersed in an external magnetic field in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity has been investigated by using the Hamilton-Jacobi method. An exact analytical solution for dependence of the minimal radius of the circular orbits ${r}_{\mathrm{mc}}$ from KS parameter $\ensuremath{\omega}$ for motion of a test particle around a spherical symmetric black hole in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity has been derived. The critical values of the particle's angular momentum for captured particles by a black hole in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity have been obtained numerically. The comparison of the obtained numerical results with the astrophysical observational data on the radii of the innermost stable circular orbits gives us the estimation of the parameter as $\ensuremath{\omega}\ensuremath{\simeq}3.6\ifmmode\cdot\else\textperiodcentered\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$.