Kerr black hole in the background of the Einstein universe
The authors investigate the Vaidya-Einstein-Kerr (VEK) black hole which represents the spacetime of the Kerr black hole in a non-vacuum, asymptotically non-flat background. The energy-momentum tensor corresponding to this spacetime satisfies reasonable energy conditions. Several properties of black holes are significantly modified by the background effects. These properties include the structure of the ergosphere, the geometry of the event horizon as well as its angular velocity. The effect of the background is investigated by computing the equatorial and polar circumferences and determining the oblateness of the horizon. The surface area of the VEK black hole gets nontrivially coupled to rotation in sharp contrast to the Kerr case. The angular velocity of the VEK horizon goes up significantly as the background influence increases. The authors describe the VEK metric as given by Vaidya and cast it in the Boyer-Lindquist form, present the energy momentum tensor and discuss the structure of the event horizon and the stationary limit surface as modified by the background. The Gaussian curvature is investigated and conditions for global embedding of the VEK black hole in Euclidean space are established.
scientific article; zbMATH DE number 2031224