Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Type D vacuum solutions: a new intrinsic approach   We present a new approach to the intrinsic properties of the type D vacuum
solutions based on the invariant symmetries that these spacetimes admit. By
using tensorial formalism and without explicitly integrating the field
equations, we offer a new proof that the upper bound of covariant derivatives
of the Riemann tensor required for a Cartan-Karlhede classification is two.
Moreover we show that, except for the Ehlers-Kundt's C-metrics, the Riemann
derivatives depend on the first order ones, and for the C-metrics they depend
on the first order derivatives and on a second order constant invariant. In our
analysis the existence of an invariant complex Killing vector plays a central
role. It also allows us to easily obtain and to geometrically interpret several
known relations. We apply to the vacuum case the intrinsic classification of
the type D spacetimes based on the first order differential properties of the
2+2 Weyl principal structure, and we show that only six classes are compatible.
We define several natural and suitable subclasses and present an operational
algorithm to detect them.

7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat