Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacetime is Locally Inertial at Points of General Relativistic Shock
  Wave Interaction between Shocks from Different Characteristic Families   We prove that spacetime is locally inertial at points of shock wave collision
in General Relativity. The result applies for collisions between shock waves
coming from different characteristic families, in spherically symmetric
spacetimes. We give a constructive proof that there exist coordinate
transformations which raise the regularity of the gravitational metric tensor
from $C^{0,1}$ to $C^{1,1}$ in a neighborhood of such points of shock wave
interaction, and a $C^{1,1}$ metric regularity suffices for locally inertial
frames to exist. This result corrects an error in our earlier RSPA-publication,
which led us to the wrong conclusion that such coordinate transformations,
which smooth the metric to $C^{1,1}$, cannot exist. Our result here proves that
regularity singularities, (a type of mild singularity introduced in our
RSPA-publication), do not exist at points of interacting shock waves from
different families in spherically symmetric spacetimes, and this generalizes
Israel's famous 1966 result to the case of such shock wave interactions. The
strategy of proof here is an extension of the strategy outlined in our
RSPA-paper, but differs fundamentally from the method used by Israel. The
question whether regularity singularities exist in more complicated shock wave
solutions of the Einstein Euler equations still remains open.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: acc-phys