Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Killing Reduction of 5-Dimensional Spacetimes   In a 5-dimensional spacetime ($M,g_{ab}$) with a Killing vector field $\xi
^a$ which is either everywhere timelike or everywhere spacelike, the collection
of all trajectories of $\xi ^a$ gives a 4-dimensional space $S$. The reduction
of ($M,g_{ab}$) is studied in the geometric language, which is a generalization
of Geroch's method for the reduction of 4-dimensional spacetime. A
4-dimensional gravity coupled to a vector field and a scalar field on $S$ is
obtained by the reduction of vacuum Einstein's equations on $M$, which gives
also an alternative description of the 5-dimensional Kaluza-Klein theory.
Besides the symmetry-reduced action from the Hilbert action on $M$, an
alternative action of the fields on $S$ is also obtained, the variations of
which lead to the same fields equations as those reduced from the vacuum
Einstein equation on $M$.

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat