Generalized Vaidya Solutions

A large family of solutions, representing, in general, spherically symmetric Type II fluid, is presented, which includes most of the known solutions to the Einstein field equations, such as, the monopolede Sitter-charged Vaidya ones. PACS numbers: 04.20Jb, 04.40.+c. ∗e-mail address: [email protected] 1 In 1951, Vaidya [1] found a solution that represents an imploding (exploding) null dust fluid with spherical symmetry. Since then, the solution has been intensively studied in gravitational collapse [2]. In particular, Papapetrou [3] first showed that this solution can give rise to the formation of naked singularities, and thus provides one of the earlier counterexamples to the cosmic censorship conjecture [4]. Later, the solution was generalized to the charged case [5]. The charged Vaidya solution soon attracted lot of attention and has been studied in various situations. For example, Sullivan and Israel [6] used it to study the thermodynamics of black holes, and Kaminaga [7] used it as a classical model for the geometry of evaporating charged black holes, while Lake and Zannias [8] studied the self-similar case and found that, similar to the uncharged case, naked singularities can be also formed from gravitational collapse. Quite recently, Husian [9] further generalized the Vaidya solution to a null fluid with a particular equation of state. Husian’s solutions have been lately used as the formation of black holes with short hair [10]. In this Letter we shall generalize the Vaidya solution to a more general case, which include most of the known solutions to the Einstein field equations, such as, the monopole-de Sitter-charged Vaidya solutions, and the Husian solutions. The generalization comes from the observation that the energy-momentum tensor (EMT) is linear in terms of the mass function. As