Schwarzschild black hole in the background of the Einstein universe: some physical effects

Abstract

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.

Influence of global cosmological expansion on local dynamics and kinematics

“…The solution proposed in the former work (Rajesh Nayak et al, 2001) is the melting of a Schwarzschild spacetime in an Einstein's static universe. This is a purely static solution whose properties and geodesics where studied in (Ramachandra and Vishveshwara, 2002). For our purposes, however, this spacetime is not interesting since it is asymptotically an Einstein universe, and hence not in agreement with the present picture of our Universe at large scales.…”

Physical effects in the Vaidya–Einstein–Kerr spacetime

“…This is the condition for the existence of null geodesics in the VES spacetime. The timelike geodesics are present within the limits given by the positive and negative roots of the equation as shown by Ramachandra and Vishveshwara [5].…”

“…In the latter it becomes even more important, especially in black-hole spacetimes wherein the Newtonian effects are considerably modified. In our investigations on circular geodesics in the VES spacetime [5] we have shown the emergence of novel features due to the asymptotically non-flat background. We now study circular geodesics in the rotating case, namely in the VEK spacetime.…”

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.…”