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In this paper the different properties of generalized Vaidya spacetime areconsidered. We located and compared different types of horizons. We show thatthe apparent horizon can contain the event horizon. The locations of all typesof horizons are compared with ones in usual Vaidya spacetime. Also, we considerthe conformal Killing vector and transform the metric to conformally-staticcoordinates. We introduce a new constant of motion along null and timelikegeodesics, which is generated by homothetic Killing vector. Theconformally-static coordinates allow to diagonalize the generalized Vaidyaspacetime. The surface gravity has been calculated for the dust and stiff fluidcases.

Generalized Vaidya spacetime: horizons, conformal symmetries, surface gravity and diagonalization