Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Restrictions on possible forms of classical matter fields carrying no
  energy   It is postulated in general relativity that the matter energy-momentum tensor
(named the stress tensor) vanishes if and only if all the matter fields vanish.
In classical lagrangian field theory the stres tensor is the variational
(symmetric) one and a priori it might occur that for some systems the tensor is
identically zero for all field configurations whereas evolution of the system
is subject to deterministic equations of motion. Such a system would not
generate its own gravitational field. To check if suchsystems may exist we find
a relationship between the stress tensor and the Euler operator. We prove that
if a system of n interacting scalar fields (n cannot exceed the spacetime
dimension d) or a single vector field (if d is even) has the stress tensor such
that its divergence is identically zero ("on and off shell"), then the Lagrange
equations of motion hold identically too. These systems are unphysical as
having no propagation equations at all. Thus nontrivial field equations imply
the nontrivial stress tensor. The theorem breaks down if the of the field
components n is greater than d. We show that for n>d matter systems without
energy and their own gravity (and yet detectable) are in principle admissible.
Their equations of motion are degenerate. We also show for which matter systems
their stress tensors cannot vanish for all solutions of the field equations.

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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex