Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3+1 Orthogonal and Conformal Decomposition of the Einstein Equation and
  the ADM Formalism for General Relativity   In this work, two particular orthogonal and conformal decompositions of the
3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for
general relativity are obtained. In order to do these, the 3+1 foliation of the
four-dimensional spacetime, the fundamental conformal transformations and the
Hamiltonian form of general relativity that leads to the ADM formalism, defined
for the conserved quantities of the hypersurfaces of the globally-hyperbolic
asymptotically flat spacetimes, are reconstructed. All the calculations up to
chapter 7 are just a review.
  We propose a method in chapter 7 which gives an interesting relation between
the Cotton (Conformal) soliton and the static vacuum solutions. The formulation
that we introduce can be extended to find the gradient Cotton soliton and the
solutions of Topologically Massive Gravity (TMG) as well as the gradient Ricci
soliton.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th