  Numerical simulation of hydrodynamic equations forms the central part of
solving various modern astrophysical problems. In the case of shocks, one can
have either dynamical equations or jump conditions (the conservation equations
without any time evolution). The solution of the jump condition in curve
space-time is derived and analyzed in detail in the present work. We also
derive the Taub adiabat or combustion adiabat equation from the jump condition.
We have analyzed both time-like and space-like shocks in the present work. We
find that the change in entropy for the weak shocks for curved space-time is
small similar to that for flat space-time. We also find that for general
relativistic space-like shocks, the Chapman-Jouguet point does not necessarily
correspond to the sonic point for downstream matter, unlike the relativistic
case. To analyze the shock wave solution for the curved space-time, one needs
the information of metric potentials describing the space-time, which for the
present work is taken to be a neutron star. We assume that a shock wave is
generated at the centre of the star and is propagating outward. As the shock
wave is propagating outwards, it combusts nuclear matter to quark matter, and
we have a combustion scenario. We find that the general relativistic treatment
of shock conditions is necessary to study shocks in neutron stars so that the
results are consistent with the solution of the TOV equation while calculating
the maximum mass for a given equation of state. We also find that with such
general relativistic treatment, the combustion process in neutron stars is
always a detonation.
