Charged Null Fluid Collapse in Anti-de Sitter Spacetimes and Naked Singularities

We investigate the occurrence of naked singularities in the spherically symmetric, plane symmetric and cylindrically symmetric collapse of charged null fluid in an antide Sitter background. The naked singularities are found to be strong in Tipler’s sense and thus violate the cosmic censorship conjecture, but not hoop conjecture. PACS number(s): 04.20.Dw That the end state of gravitational collapse of a sufficiently massive star is a gravitational singularity is a fact established by the singularity theorems of Hawking and Ellis [1]. However, these singularities theorems does not guarantee the existence of an event horizon. The conjecture that such a singularity from a regular initial surface must always be hidden behind an event horizon, called cosmic censorship conjecture (CCC) was proposed by Penrose [2]. The CCC forbids the existence of naked singularities. Despite almost 30 years of effort we are far from a general proof of CCC (for recent reviews and references, see [3]). But, significant progress has been made in trying to find counter examples to CCC. In particular, the Vaidya [4] solution that represent an imploding null fluid with spherical symmetry has been intensively studied for the formation of naked singularities [5]. Many of studies in the gravitational collapse were motivated by Thorne’s is hoop conjecture [6] that collapse will yield a black hole only if a mass M is compressed to a region with circumference C ≤ 4πM in all directions. If hoop conjecture is true, naked singularities may form if collapse can yield C ≥ 4πM in some direction. Thus, planar or cylindrical matter will not form a black hole (black plane or black string) [6]. However hoop conjecture was given for spacetimes with a zero cosmological term. In the presence of negative cosmological term one can expect the occurrence of major changes. ∗email: [email protected]