Analytic derivation of the map of null rays passing near a naked singularity - art. no. 124021

Recently the energy emission from a naked singularity forming in spherical dust collapse has been investigated. This radiation is due to particle crea tion in a curved spacetime. In this discussion, the central role is played by the mapping formula between the incoming and the outgoing null coordinat es. For the self-similar model, this mapping formula has been derived analy tically. But for the model with C-infinity density profile, the mapping for mula has been obtained only numerically. In the present paper, we argue tha t the singular nature of the mapping is determined by the local geometry ar ound the point at which the singularity is first formed. If this is the cas e, it would be natural to expect that the mapping formula can be derived an alytically. In the present paper, we analytically rederive the same mapping formula for the model with C-infinity density profile that has been earlie r derived using a numerical technique.