Kerr Black Hole in the Background of the Einstein Universe

Influence of global cosmological expansion on local dynamics and kinematics

“…) Other solutions, modeling a black hole in a cosmological spacetime, have been given in the literature. However, these solutions model objects which are either rotating (Ramachandra et al, 2003;Vaidya, 1977Vaidya, , 1984, charged (Gao and Zhang, 2004), or both (Patel and Trivedi, 1982). Surveys on the subject of cosmological black holes are (Vishveshwara, 2000) and (McClure, 2006).…”

Physical effects in the Vaidya–Einstein–Kerr spacetime

“…The gyroscopic frequency ∓|τ 1 | is about the basis e (3) which is oriented along the zdirection. The orbiting (co-rotating) observer measures precession relative to the basis e (1) which coincides with the radius vector which rotates with the angular velocity given by equation (2.13). The precession angle per unit time as evaluated in the rotating coordinates is…”

“…However, the introduction of the non-flat background leads to non-trivial modifications of the results obtained in the flat case. In a previous paper [1], we have investigated the geometry of the event horizon of the Kerr black hole in the background of the Einstein universe given by Vaidya [2] or the Vaidya-Einstein-Kerr black hole (this spacetime is hereafter referred to as the VEK spacetime) and showed that many of the usual results are radically altered by the presence of the non-flat background. Therefore, it would be interesting and instructive to study some examples of physical effects in the VEK spacetime as well.…”

The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

“…In a series of studies [7][8][9][10] we have been investigating non-vacuum black holes in non-flat backgrounds in order to compare and contrast the nature and features of such black holes with their usual counterparts. Focusing on the Vaidya-Einstein-Schwarzschild (VES) and the Vaidya-Einstein-Kerr (VEK) black holes which essentially represent nonvacuum black holes in the background of the Einstein universe [11], we have showed [8][9][10] that much insight may be gained by studying the non-flat versions of the classical tests, the nature of circular geodesics as well as physical effects such as gyroscopic precession. In the present paper we investigate in detail the existence of the Carter constant and the Petrov classification of the above non-vacuum, non-flat spacetimes.…”

“…In the present paper we investigate some of these issues in the context of the nonvacuum, stationary, axisymmetric Kerr black hole in the background of the Einstein universe given by Vaidya [11] or the Vaidya-Einstein-Kerr (VEK) black hole [9] as already mentioned above. We show that in spite of the absence of the features of vacuum and asymptotic flatness both the separability property and the type-D nature of the spacetime hold.…”