Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free and constrained symplectic integrators for numerical general
  relativity   We consider symplectic time integrators in numerical General Relativity and
discuss both free and constrained evolution schemes. For free evolution of
ADM-like equations we propose the use of the Stoermer-Verlet method, a standard
symplectic integrator which here is explicit in the computationally expensive
curvature terms. For the constrained evolution we give a formulation of the
evolution equations that enforces the momentum constraints in a holonomically
constrained Hamiltonian system and turns the Hamilton constraint function from
a weak to a strong invariant of the system. This formulation permits the use of
the constraint-preserving symplectic RATTLE integrator, a constrained version
of the Stoermer-Verlet method.
  The behavior of the methods is illustrated on two effectively 1+1-dimensional
versions of Einstein's equations, that allow to investigate a perturbed
Minkowski problem and the Schwarzschild space-time. We compare symplectic and
non-symplectic integrators for free evolution, showing very different numerical
behavior for nearly-conserved quantities in the perturbed Minkowski problem.
Further we compare free and constrained evolution, demonstrating in our
examples that enforcing the momentum constraints can turn an unstable free
evolution into a stable constrained evolution. This is demonstrated in the
stabilization of a perturbed Minkowski problem with Dirac gauge, and in the
suppression of the propagation of boundary instabilities into the interior of
the domain in Schwarzschild space-time.

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The categories of this paper are: cs
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: physics