Physics
Scientific paper
Oct 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977zhetf..73.1201b&link_type=abstract
Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki, vol. 73, Oct. 1977, p. 1201-1215. In Russian.
Physics
11
Einstein Equations, Hydrodynamic Equations, Relativity, Shock Wave Propagation, Spherical Waves, Asymptotic Methods, Flow Velocity, Gas Flow, Topology, Trajectory Analysis
Scientific paper
The paper investigates self-similar spherically symmetric solutions to the Einstein equations and hydrodynamic equations describing the propagation of a shock wave in an ultrarelativistic gas with an equation of state p = k x epsilon (where p is pressure, epsilon is energy density and k is between 0 and 1). In a metric of self-similar solutions in conformally static form, the Einstein equations and the hydrodynamic equations are examined on the basis of the qualitative theory of differential equations. Solutions are obtained with a divergent shock wave (solution of the self-similar problem of an explosion in general relativity) and with a collapsing shock wave, arising during collapse in the presence of pressure.
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