  Type I X-ray bursts are thermonuclear burning events which occur on the
surfaces of accreting neutron stars. Burning begins in a localised spot in the
star's ocean layer before propagating across the entire surface as a
deflagration. On the scale of the entire star, the burning front can be thought
of as discontinuity. To model this, we investigated the reactive Riemann
problem for relativistic deflagrations and detonations and developed a
numerical solver. Unlike for the Newtonian Riemann problem, where only the
velocity perpendicular to the interface is relevant, in the relativistic case
the tangential velocity becomes coupled through the Lorentz factor and can
alter the waves present in the solution. We investigated whether a fast
tangential velocity may be able to cause a deflagration wave to transition to a
detonation. We found that such a transition is possible, but only for
tangential velocities that are a significant fraction of the speed of light or
for systems already on the verge of transitioning. Consequently, it is highly
unlikely that this transition would occur for a burning front in a neutron star
ocean without significant contributions from additional multidimensional
effects.
