Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kerr-Schild ansatz revised   Kerr-Schild metrics have been introduced as a linear superposition of the
flat spacetime metric and a squared null vector field, say $\boldsymbol{k}$,
multiplied by some scalar function, say $H$. The basic assumption which led to
Kerr solution was that $\boldsymbol{k}$ be both geodesic and shearfree. This
condition is relaxed here and Kerr-Schild ansatz is revised by treating
Kerr-Schild metrics as {\it exact linear perturbations} of Minkowski spacetime.
The scalar function $H$ is taken as the perturbing function, so that Einstein's
field equations are solved order by order in powers of $H$. It turns out that
the congruence must be geodesic and shearfree as a consequence of third and
second order equations, leading to an alternative derivation of Kerr solution.

10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org