Propagation of a Shock Wave in General Relativity: Stationary Approximation

Normal propagation of a shock wave in general relativity through the inhomogeneous gases is considered. Approximation in which the equillibrium medium is devided into infinitesimal layer of a uniform density (the Chisnell-Ôno method) is applied. In general relativity, energy induces a gravitational force and matter deforms space-time. Both these effects are included simply in determining propagation of a shock wave. It is found that the grouwth of strength of the shock wave due to pressure gradient is suppressed compared with the Newtonian case. Both effects have influence on propagation of the shock wave near the surface of a star where shock strength becomes large. However, the effect owing to gravitational field induced by pressure is rather larger than that by deformation of the space-time. As an example propagation of the shock wave in the neutron star is calculated numerically and it is shown that shock strength is estimated to be 10–20% small compared with that in flat space-time.