The high velocities observed in supernovae require a relativistic treatment for the equation of motion in the presence of gradients in the density of the interstellar medium .
The adopted theory is that of the thin layer approximation .
The chosen medium is auto-gravitating with respect to an equatorial plane .
The differential equation which governs the relativistic conservation of momentum is solved in numerically and by recursion .
The asymmetric field of relativistic velocities as well the time dilation are plotted at the age of 1 yr for SN 1987A .