Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free evolution of the hyperboloidal initial value problem in spherical
  symmetry   The hyperboloidal initial value problem is addressed in the context of
Numerical Relativity, motivated by its use of hyperboloidal slices - smooth
spacelike slices that reach future null infinity, the "place" in spacetime
where radiation is to be extracted. This is beneficial for studying the global
properties of isolated systems and unambiguously extracting their gravitational
radiation. The present approach implements the Einstein equations as a free
evolution, using the BSSN and Z4 formulations (standard in current codes)
expressed in terms of a conformally rescaled metric as suggested by Penrose,
and with a time-independent conformal factor. The main difficulty is that the
resulting system of PDEs includes formally divergent terms at null infinity
that require a special treatment. The numerical simulations in this thesis are
restricted to spherical symmetry, although the regularization in the radial
direction is expected to also apply to the full 3D case up to some extent. A
critical ingredient are the gauge conditions, which rely on well-chosen source
functions and damping terms and control the treatment of future null infinity
by means of the scri-fixing condition. Once the numerical implementation was
stabilized, stable numerical evolutions of a massless scalar field coupled to
the Einstein equations could be performed with regular and black hole trumpet
initial data on a hyperboloidal slice. The signal of the scalar field has been
successfully extracted at future null infinity. Small perturbations of regular
initial data give stationary data that are stable forever, while larger scalar
field perturbations result in the formation of a black hole. Schwarzschild
trumpet initial data have been found to slowly drift away from the expected
stationary values, but for small perturbations the effect is slow enough to
allow the observation of the power-law decay tails of the scalar field.

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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th