Particle motion around black hole in Hořava-Lifshitz gravity

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 Hořava-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 Hořava-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 $\omega$ for motion of a test particle around a spherical symmetric black hole in Hořava-Lifshitz gravity has been derived. The critical values of the particle’s angular momentum for captured particles by a black hole in Hořava-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 $\omega \simeq 3.6·{10}^{-24}{\mathrm{cm}}^{-2}$.

Figure 1

Radial dependence of the effective potential of the radial motion of the charged particle around a black hole immersed in a uniform magnetic field in Hořava-Lifshitz gravity. In the left graph, the effective potential of the radial motion of the charged particle around a black hole has been shown for the different values of the dimensionless parameter $\tilde{\omega }$; the values of the momentum $\mathcal{L}/mM=4.3$ and the magnetic parameter $ϵ=0.03$ are fixed. For comparison, we have also plotted this dependence in the case of the Schwarzschild black hole, corresponding to $\tilde{\omega }\gg 1$. In the right graph, the effective potential of the radial motion of the charged particle around a black hole has been shown for the different values of the magnetic parameter $ϵ$; the values of the momentum $\mathcal{L}/mM=4.3$ and the dimensionless parameter $\tilde{\omega }=1$ are fixed.

Figure 2

Radial dependence of energy (left graph) and angular momentum (right graph) of the circular orbits around a black hole in Hořava-Lifshitz gravity for the different values of the dimensionless parameter $\tilde{\omega }$. For comparison, we have also plotted this dependence in the case of the Schwarzschild black hole, corresponding to $\tilde{\omega }\gg 1$.

Figure 3

Dependence of the radius of the horizon and $r_{\mathrm{mc}}$ from the $\tilde{\omega }$.

Figure 4

Dependence of the ISCO radius from the $\tilde{\omega }$.