Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetries of the Trautman retarded radial coordinates   We consider spacetime described by observer that uses Trautman's retarded
radial coordinates system. Given a metric tensor, we find all the symmetry
maps. They set a 10 dimensional family of local diffeomorphisms of spacetime
and can be parametrized by the Poincar\'e algebra. This result is similar to
the symmetries of a Gauss observer using the Gauss simultaneous radial
coordinates and experiencing the algebra deformation induced by the spacetime
Riemann tensor. A new, surprising property of the retarded coordinates is that
while the symmetries are differentiable, in general they are not differentiable
twice. In other words, a family of smooth symmetries is smaller than in the
Gaussian case. We demonstrate examples of that non-smoothness and find
necessary conditions for the differentiability to the second order. We also
discuss the consequences and relevance of that result for geometric relational
observables program. One can interpret our result as that the retarded radial
coordinates provide gauge conditions stronger that the Gaussian 4d radial
gauge.

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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn