Shock Wave Interactions in General Relativity and the Emergence of Regularity Singularities

Released on by Moritz Andreas Reintjes
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  • Shock Wave Interactions in General Relativity and the Emergence of Regularity Singularities Book Detail

  • Author : Moritz Andreas Reintjes
  • Release Date : 2011
  • Publisher :
  • Genre :
  • Pages :
  • ISBN 13 : 9781267240712
  • File Size : 66,66 MB
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Shock Wave Interactions in General Relativity and the Emergence of Regularity Singularities by Moritz Andreas Reintjes PDF Summary

Book Description: We show that the regularity of the gravitational metric tensor cannot be lifted from C(0,1) to C(1,1) by any C(1,1) coordinate transformation in a neighborhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel's Theorem which states that such coordinate transformations always exist in a neighborhood of a point on a smooth single shock surface. The results thus imply that points of shock wave interaction represent a new kind of singularity in spacetime, singularities that make perfectly good sense physically, that can form from the evolution of smooth initial data, but at which the spacetime is not locally Minkowskian under any coordinate transformation. In particular, at such singularities, delta function sources in the second derivatives of the gravitational metric tensor exist in all coordinate systems, but due to cancelation, the curvature tensor remains uniformly bounded.

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Shock Wave Interactions

Shock Wave Interactions

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This edited monograph contains the proceedings of the International Shock Interaction Symposium, which emerged as an heir to both the Mach Reflection and Shock