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 $g_{t\varphi }$ 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 $\eta$ 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 ${\Omega }_H$, the Kepler's third law, the innermost stable circular orbit and the radiative efficiency $\epsilon$ in the thin accretion disk model. Our results also show that for the phantom black hole the radiative efficiency $\epsilon$ is positive only for the case $\eta \le {\eta }_c$. The threshold value ${\eta }_c$ increases with the rotation parameter $a$.

14 pages, 6 figures

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