  The gravitational collapse of a high-density null charged matter fluid,
satisfying the Hagedorn equation of state, is considered in the framework of
the Vaidya geometry. The general solution of the gravitational field equations
can be obtained in an exact parametric form. The conditions for the formation
of a naked singularity, as a result of the collapse of the compact object, are
also investigated. For an appropriate choice of the arbitrary integration
functions the null radial outgoing geodesic, originating from the shell
focussing central singularity, admits one or more positive roots. Hence a
collapsing Hagedorn fluid could end either as a black hole, or as a naked
singularity. A possible astrophysical application of the model, to describe the
energy source of gamma-ray bursts, is also considered.
