Gravitational field of a slowly rotating black hole with phantom global monopole

Abstract

We present a slowly rotating black hole with phantom global monopole by solving Einstein's field equation and find that presence of global monopole changes the structure of black hole. The metric coefficient $g_{tϕ}$ contains hypergeometric function of the polar coordinate $r$, which is more complex than that in the usual slowly rotating black hole. The energy scale of symmetry breaking $η$ affects the black hole horizon and a deficit solid angle. Especially, the solid angle is surplus rather than deficit for a black hole with the phantom global monopole. We also study the correction originating from the global monopole to the angular velocity of the horizon $Ω_H$, the Kepler's third law, the innermost stable circular orbit and the radiative efficiency $ε$ in the thin accretion disk model. Our results also show that for the phantom black hole the radiative efficiency $ε$ is positive only for the case $η\leq η_c$. The threshold value $η_c$ increases with the rotation parameter $a$.