Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solution of a Neumann boundary value problem for the stationary
  axisymmetric Einstein equations   For a stationary and axisymmetric spacetime, the vacuum Einstein field
equations reduce to a single nonlinear PDE in two dimensions called the Ernst
equation. By solving this equation with a {\it Dirichlet} boundary condition
imposed along the disk, Neugebauer and Meinel in the 1990s famously derived an
explicit expression for the spacetime metric corresponding to the
Bardeen-Wagoner uniformly rotating disk of dust. In this paper, we consider a
similar boundary value problem for a rotating disk in which a {\it Neumann}
boundary condition is imposed along the disk instead of a Dirichlet condition.
Using the integrable structure of the Ernst equation, we are able to reduce the
problem to a Riemann-Hilbert problem on a genus one Riemann surface. By solving
this Riemann-Hilbert problem in terms of theta functions, we obtain an explicit
expression for the Ernst potential. Finally, a Riemann surface degeneration
argument leads to an expression for the associated spacetime metric.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg