Solving the relativistic rankine-hugoniot condition in presence of magnetic field in astrophysical scenario

Rankine-Hugoniot condition has been solved to study phase transition in astrophysical scenario mainly in the case of phase transition from neutron star (NS) to quark star (QS). The phase transition is brought about by a combustion front, which travels from the center to the surface. The equations of state and temperature plays a huge role in determining the nature of the front propagation, which brings about the phase transition in neutron stars (NSs). Magnetic field has been introduced and the modified conservation condition for the perpendicular and oblique shocks is obtained. Numerical solution of the perpendicular shock has been shown in the figures, which finds that the magnetic field helps in shock generation. It indirectly hints at the instability of the matter and thereby the NS for very high magnetic field, implying that NSs can only support finite magnetic field strength.