The relativistic three dimensional evolution of SN 1987A

TL;DR

This paper models the relativistic evolution of supernova SN 1987A using the thin layer approximation, accounting for density gradients and asymmetries, and presents numerical solutions and velocity field plots at one year.

Contribution

It introduces a relativistic model for supernova evolution with asymmetric velocity fields, solved numerically, specifically applied to SN 1987A.

Findings

Relativistic velocities are asymmetric in the model.

Numerical solutions match observed supernova dynamics.

Time dilation effects are analyzed at one year.

Abstract

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.