Geometric properties of magnetized black hole event horizons and ergosurfaces

Abstract

In this paper we focus in the geometric properties of the magnetized Kerr-Newman metric. Three applications are considered. First, the event horizon surface area is calculated and from there we derive the first law of thermodynamics for magnetized black holes. We have obtained analytical expressions for the surface gravity, angular velocity, electric potential, and magnetic moment at the magnetized Kerr-Newman black hole event horizon. An approximate expression for the surface area of the magnetized black hole ergosurface was also obtained. Second, we study the magnetized Kerr-Newman black hole's circumferences. We found that for small values of the angular momentum (| | < 0.1) the event horizon has a prolate spheroid shape. Increasing the value of the angular momentum will change the event horizon shape from a prolate ellipsoid to an oblate spheroid. For small values of the angular momentum and charge the ergosurface shape is an oblate spheroid. Increasing these two parameters will change the ergosurface shape from a oblate spheroid to a prolate spheroid. Third, analytical expressions for the magnetized Kerr-Newman event horizon and ergosurface Gaussian curvatures were obtained although not explicitly shown. Instead a graphical analysis was carried out to visualize regions where Gaussian curvatures take negative or positive values. We found that the Gaussian curvature at the event horizon poles has negative values and do not satisfy Pelavas condition. Therefore, these regions can not be embedded in E3. However, the magnetized Kerr-Newman ergosurface can be embedded in E3 regardless the negative Gaussian curvature values in some regions of the ergosurface.