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

Abstract

We present a slowly rotating black hole solution with a phantom global monopole by solving Einstein's field equation and find that the presence of the global monopole changes the black hole structure. The metric coefficient gtϕ contains the 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 the deficit solid angle. In particular, the solid angle is surplus rather than deficit for the black hole with the phantom global monopole. We also study the effects of the global monopole on the angular velocity of the horizon ΩH, Kepler's third law, the innermost stable circular orbit and the radiative efficiency ϵ in the thin accretion disc model. Our results also show that for a phantom black hole, the radiative efficiency ϵ is positive only in the case η ⩽ ηc. The threshold value ηc increases with the rotation parameter a.