Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravity, Stability and Energy Conservation on the Randall-Sundrum
  Brane-World   We carefully investigate the gravitational perturbation of the
Randall-Sundrum (RS) single brane-world solution [hep-th/9906064], based on a
covariant curvature tensor formalism recently developed by us. Using this
curvature formalism, it is known that the `electric' part of the 5-dimensional
Weyl tensor, denoted by $E_{\mu\nu}$, gives the leading order correction to the
conventional Einstein equations on the brane. We consider the general solution
of the perturbation equations for the 5-dimensional Weyl tensor caused by the
matter fluctuations on the brane. By analyzing its asymptotic behaviour in the
direction of the 5th dimension, we find the curvature invariant diverges as we
approach the Cauchy horizon. However, in the limit of asymptotic future in the
vicinity of the Cauchy horizon, the curvature invariant falls off fast enough
to render the divergence harmless to the brane-world. We also obtain the
asymptotic behavior of $E_{\mu\nu}$ on the brane at spatial infinity, assuming
the matter perturbation is localized. We find it falls off sufficiently fast
and will not affect the conserved quantities at spatial infinity. This
indicates strongly that the usual conservation law, such as the ADM energy
conservation, holds on the brane as far as asymptotically flat spacetimes are
concerned.

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The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph