Abstract:
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 Vaidya–Einstein–Schwarzschild spacetime. We demonstrate explicitly that both spacetimes are of type-D.
