Amendment 1
published on 31 Aug 2001:
Description
Now minimal surface scheme is attributed to Neugebauer and
Herold [47] instead of Wu et al. [24]. Section 2.4.4 has been
renamed from Wu et al. (WMSHR) to Neugebauer and Herold (NH), and
reference 24 substituted by reference 47 in 1st paragraph as well
as in subsection 2.4.4, and reference to Wu et al.[24] has been
moved to later sentence in the same subsection.
Old version
as published on 18 Jun 1998:
Out of the ten components of the field equations that describe
the geometry of a rotating relativistic star, only four are
independent; one has the freedom to choose which four components
to use. After choosing four field equations, there are different
methods one can use to solve them. First models were obtained by
Wilson [19] and Bonazzola and Schneider [20]. Here we will review
the following methods: Hartle's slow rotation formalism, the
Newton-Raphson linearization scheme due to Butterworth and Ipser
[21
], a scheme using Green's functions by Komatsu et al. [22
, 23
], a minimal surface scheme due to Wu et al. [24
], and two spectral methods by Bonazzola et al. [25
, 26
]. Below we give a description about each method and its various
implementations (codes).
(...)
The numerical scheme by Wu et al. [24] implements the minimal
surface formalism for rotating axisymmetric space-times [44, 45,
46], in which Einstein's field equations are equivalent to the
minimal surface equations in an abstract Riemannian potential
space with a well-defined metric, whose coordinates are the four
metric functions of the usual stationary, axisymmetric metric. A
finite element technique is used, and the system of equations is
solved by a Newton-Raphson method. Models based on realistic EOSs
are presented in [47]. The WMSHR code has been used to visualize
rapidly rotating stars by embedding diagrams and 4D-ray-tracing
pictures (See [48] for a review.). (...) "
Editorial comment:
Change requested by author on 27 Oct 1998
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Rotating Stars in Relativity
Nikolaos Stergioulas
Publication No. 1998-8 (Amendment 1/31 Aug 2001)
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