4 Rotating Stars in Numerical Relativity

Recently, the dynamical evolution of rapidly rotating stars has become possible in numerical relativity. In the framework of the 3+1 split of the Einstein equations [283], a stationary axisymmetric star can be described by a metric of the standard form

2 2 i 2 i i j ds = − (α − βiβ )dt + 2βidx dt + γijdx dx , (57 )
where α is the lapse function, βi is the shift three-vector, and γij is the spatial three-metric, with i = 1 ...3. The spacetime has the following properties:

Crucial ingredients for the successful long-term evolutions of rotating stars in numerical relativity are the conformal ADM schemes for the spacetime evolution (see [233275284]) and hydrodynamical schemes that have been shown to preserve well the sharp rotational profile at the surface of the star [106Jump To The Next Citation Point293Jump To The Next Citation Point105Jump To The Next Citation Point].

 4.1 Numerical evolution of equilibrium models
  4.1.1 Stable equilibrium
  4.1.2 Instability to collapse
  4.1.3 Dynamical bar-mode instability
 4.2 Pulsations of rotating stars
 4.3 Rotating core collapse
  4.3.1 Collapse to a rotating black hole
  4.3.2 Formation of rotating neutron stars

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