image 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:

"2.4 Numerical Schemes

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 Jump To The Next Citation Point In The Article], a scheme using Green's functions by Komatsu et al. [22 Jump To The Next Citation Point In The Article, 23 Jump To The Next Citation Point In The Article], a minimal surface scheme due to Wu et al. [24 Jump To The Next Citation Point In The Article], and two spectral methods by Bonazzola et al. [25 Jump To The Next Citation Point In The Article, 26 Jump To The Next Citation Point In The Article]. Below we give a description about each method and its various implementations (codes).

(...)

2.4.4 Wu et al. (WMSHR)

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
image Rotating Stars in Relativity
Nikolaos Stergioulas
Publication No. 1998-8 (Amendment 1/31 Aug 2001)