Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the relation between the Einstein field equations and the
  Jacobi-Ricci-Bianchi system   The 1+3 covariant equations, embedded in an extended tetrad formalism and
describing a space-time with an arbitrary energy-momentum distribution, are
reconsidered. It is shown that, provided the 1+3 splitting is performed with
respect to a generic timelike congruence with tangent vector u, the Einstein
field equations can be regarded as the integrability conditions for the Jacobi
and Bianchi equations together with the Ricci equations for u. The same
conclusion holds for a generic null congruence in the Newman-Penrose framework.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas