Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solution-generating methods of Einstein's equations by Hamiltonian
  reduction   The purpose of this paper is to demonstrate a new method of generating exact
solutions to the Einstein's equations obtained by the Hamiltonian reduction.
The key element to the successful Hamiltonian reduction is finding the
privileged spacetime coordinates in which physical degrees of freedom
manifestly reside in the conformal two-metric, and all the other metric
components are determined by the conformal two-metric. In the privileged
coordinates the Einstein's constraint equations become trivial; the Hamiltonian
and momentum constraints are simply the defining equations of a non-vanishing
gravitational Hamiltonian and momentum densities in terms of conformal
two-metric and its conjugate momentum, respectively. Thus, given any conformal
two-metric, which is a constraint-free data, one can construct the whole
4-dimensional spacetime by integrating the first-order superpotential
equations. As the first examples of using Hamiltonian reduction in solving the
Einstein's equations, we found two exact solutions to the Einstein's equations
in the privileged coordinates. Suitable coordinate transformations from the
privileged to the standard coordinates show that they are just the
Einstein-Rosen wave and the Schwarzschild solution. The local gravitational
Hamiltonian and momentum densities of these spacetimes are also presented in
the privileged coordinates.

29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga