General Relativistic Shock Waves that Extend the Oppenheimer-Snyder Model
نویسنده
چکیده
In earlier work we constructed a class of spherically symmetric, ̄uid dynamical shock waves that satisfy the Einstein equations of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. Our shock waves are determined by a system of ordinary dierential equations that describe the matching of a FriedmannRobertson-Walker metric (a cosmological model for the expanding universe) to an Oppenheimer-Tolman metric (a model for the interior of a star) across a shock interface. In this paper we derive an alternate version of these ordinary dierential equations, which are used to demonstrate that our theory generates a large class of physically meaningful (Lax-admissible) outgoing shock waves that model blast waves in a general relativistic setting. We also obtain formulas for the shock speed and other important quantities that evolve according to the equations. The resulting formulas are important for the numerical simulation of these solutions.
منابع مشابه
Shock-Wave Solutions in Closed Form and the Oppenheimer-Snyder Limit in General Reality
In earlier work the authors derived a set of ODEs that describe a class of spherically symmetric, fluid dynamical shock-wave solutions of the Einstein equations. These solutions model explosions in a general relativistic setting. The theory is based on matching Friedmann–Robertson– Walker (FRW) metrics (models for the expanding universe) to Oppenheimer–Tolman (OT) metrics, (models for the inter...
متن کاملExperimental analysis of shock waves turbulence in contractions with rectangular sections
Formation of shock waves has an important role in supercritical flows studies. These waves are often occurring during passage of supercritical flow in the non-prismatic channels. In the present study, the effect of length of contraction wall of open-channel for two different geometries (1.5 m and 0.5 m) and fixed contraction ratio was investigated on hydraulic parameters of shock waves using ex...
متن کاملShock-wave cosmology inside a black hole.
We construct a class of global exact solutions of the Einstein equations that extend the Oppeheimer-Snyder model to the case of nonzero pressure, inside the black hole, by incorporating a shock wave at the leading edge of the expansion of the galaxies, arbitrarily far beyond the Hubble length in the Friedmann-Robertson-Walker (FRW) spacetime. Here the expanding FRW universe emerges be-hind a su...
متن کاملShock-Wave Solutions of the Einstein Equations." The Oppenheimer-Snyder Model of Gravitational Collapse Extended to the Case of Non-Zero Pressure
متن کامل
Self-similar Evolution of Relativistic Shock Waves Emerging from Plane-parallel Atmospheres
We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there is a self-similar motion of the fluid before and after the shock emergence. The time evolution of the Lorentz factor of the shock front is assumed to follow ...
متن کامل