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

TL;DR

This paper derives a new model of a slowly rotating black hole with a phantom global monopole, revealing unique effects on the black hole's structure, horizon, and accretion disk properties due to the monopole's influence.

Contribution

It introduces a novel solution for a slowly rotating black hole with a phantom global monopole, highlighting the complex metric and its impact on black hole characteristics.

Findings

Global monopole alters black hole structure and horizon.

Surplus solid angle observed in the presence of phantom monopole.

Radiative efficiency depends on symmetry breaking scale and rotation.

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 $g_{t\phi}$ 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 $\eta\leq \eta_c$. The threshold value $\eta_c$ increases with the rotation parameter $a$.