We investigate the acceleration of shock waves to relativistic velocities in the outer layers of exploding stars .
By concentrating the energy of the explosion in the outermost ejecta , such trans-relativistic blast waves can serve as the progenitors of gamma-ray bursts ( GRBs ) ; in particular , the “ baryon-loading ” problem that plagues many models of GRBs is circumvented .
Postshock acceleration is effective in boosting the kinetic energy in relativistic ejecta .
We present physically motivated analytic expressions to describe trans-relativistic blast waves in supernovae , and we validate these expressions against numerical simulations of test problems .
Investigating the effect of stellar structure on mass ejection , we find that relativistic ejecta are enhanced in more centrally condensed envelopes—e.g. , for radiative envelopes , when the luminosity approaches the Eddington limit .
Convenient formulae are presented with which to estimate the production of relativistic ejecta from a given progenitor .

We apply our analytic and numerical methods to a model of SN 1998bw , finding significantly enhanced relativistic ejecta compared to previous studies .
We propose that GRB 980425 is associated with SN 1998bw and may have resulted from an approximately spherical explosion producing \sim 10 ^ { -6 } \ > { M _ { \odot } } of mildly relativistic ejecta with mean Lorentz factor \bar { \Gamma } \sim 2 , which then interacted with a dense circumstellar wind with mass loss rate \sim { few } \times 10 ^ { -4 } \ > { M _ { \odot } \ > yr ^ { -1 } } .
A highly asymmetric explosion is not required .
An extreme model of “ hypernova ” explosions in massive stars is able to account for the energetics and relativistic ejecta velocities required by many of the observed cosmological GRBs .
However , the most energetic bursts require asymmetric expulsion of ejecta , perhaps caused by rotationally flattened progenitors .
We present simplified models and simulations of explosions resulting from accretion-induced collapse of white dwarfs and phase transitions of neutron stars .
While we find increased energies in relativistic ejecta compared to previous studies , these explosions are unlikely to be observed at cosmological distances with current detectors , unless extreme explosion energies and asymmetries are invoked .