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A prototype of an asymptotically non-flat black hole spacetime is that of a Schwarzschild black hole in the background of the Einstein universe, which is a special case of the representation of a black hole in a cosmological background given by Vaidya. Recently, this spacetime has been studied in detail by Nayak et al. They constructed a composite spacetime called the Vaidya–Einstein–Schwarzschild (VES) spacetime. We investigate some of the physical effects inherent to this spacetime. We carry out a background–black hole decomposition of the spacetime in order to separate out the effects due to the background spacetime and the black hole. The physical effects we study include the classical tests—the gravitational redshift, perihelion precession and light bending—and circular geodesics. A detailed classification of geodesics, in general, is also given.

The existence of the Carter constant in the Vaidya-Einstein-Kerr (VEK) spacetime and its relation to the Petrov type is investigated. This spacetime is an example of a black hole in an asymptotically non-flat background. We construct the Carter constant and obtain the Killing tensor in the VEK spacetime. The Newman-Penrose formalism is employed to obtain the spin coefficients. We present a complete (Petrov) classification of the VEK spacetime and the special case of the non-rotating VaidyaEinstein-Schwarzschild spacetime. We demonstrate explicitly that both spacetimes are of type-D.

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We investigate some physical effects in the Vaidya–Einstein–Kerr (VEK) spacetime which represents the spacetime of the Kerr black-hole in the background of the non-flat Einstein universe. We have chosen for our study the nature of circular geodesics and the phenomenon of gyroscopic precession in the VEK spacetime. We show that the nature of the circular geodesics is radically altered by the presence of the background. Turning to gyroscopic precession we show that a novel feature emerges in that the background affects the precession in two different ways, one by coupling to rotation and another in a direct manner. We investigate also several special cases of general precession.

This is a summary of the papers presented in session W1 on the papers submitted to the workshop I on the classical aspects of black holes and compact objects were classified into three categories: (i) theoretical aspects; (ii) astrophysical aspects; (iii) gravitational radiation. The three sessions were devoted each to one of the above categories. The chairmen of the workshop were J Bičák, Charles University, Prague (Czech Republic) and C V Vishveshwara, Indian Institute of Astrophysics, India. List of contributions to Workshop I Theoretical aspects(a) No scalar hair theorem for charged black holes in scalar tensor theories, by

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