Naked Singularity In Generalized Vaidya Spacetime

ABSTRACT

In this study we find the conditions of mass function for the formation and existence of naked singularity of the metric given in generalized Vaidya spacetime. We study and clarify how naked singularity is brought about interms of the apparent and event horizon. We analyse the components of the metric as given in the Vaidya spacetime equation. We consider the collapsing model in which the imploding radiation collapses at the center of symmetry in the universe through which we derive the radial null geodesics with the help of the Euler - Lagrange equation. The solution to the radial null geodesics is obtained after simplifying the DE obtained so that we come to the quadratic equation whose trace, determinant as well as the discriminant are greater or equal to zero which enable us to state the nature of DE to be a node. Then, the choice of mass function is made to express the structure of the singularity at the origin in terms of mass function. The results obtained are consistent with that of Maombi et al. The nature of tangent of the non-spacelike geodesics at the singularity has been put into consideration to determine the condition of outgoing radial non-spacelike geodesics. The L’Hospital’s rule has been used to express the radial null-geodesics in the quadratic equation from which the graph of the apparent horizon against the tangential radial null geodesics as generated from Matlab shows the existence of outgoing null rays that cross over the singularity leading to the naked singularity formation. The L’Hospital’s rule again has been used to evaluate the limits along non - spacelike geodesics as to determine the strength of the naked singularity so formed in a generalized Vaidya spacetime.