Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Modified Variational Principle in Relativistic Hydrodynamics.
  I.Commutativity and Noncommutativity of the Variation Operator with the
  Partial Derivative   A model is proposed, according to which the metric tensor field in the
standard gravitational Lagrangian is decomposed into a projection (generally -
with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary
4-vector field and a tensor part along the same vector field. A theorem has
been used, according to which the variation and the partial derivative, when
applied to a tensor field, commute with each other if and only if the tensor
field and its variation have zero covariant derivatives, provided also the
connection variation is zero. Since the projection field obviously does not
fulfill the above requirements of the ''commutation'' theorem, the exact
expression for the (non-zero) commutator of the variation and the partial
derivative, applied to the projection tensor field, can be found from a set of
the three defining equations. The above method will be used to construct a
modified variational approach in relativistic hydrodynamics, based on variation
of the vector field and the projection field, the last one thus accounting for
the influence of the reference system of matter (characterized by the 4-vector)
on the gravitational field.

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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: eess