General Relativistic Collapse of Axially Symmetric Stars Leading to the Formation of Rotating Black Holes

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Abstract
Numerical calculations have been made for the formation process of axisymmetric, rotating black holes of 10M⊙. The initial density of a star is about 3×1013 g/cm3. Numerical results are classified mainly by q which corresponds to |a|/M in a Kerr black hole. For q ≲ 0.3, the effect of rotation to the gravitational collapse is only to make the shape of matter oblate. For 0.3 ≲ q≤0.95, although the distribution of matter is disk-like, a ring-like peak of proper density appears. This ring is inside the apparent horizon, which is always formed in the case q ≲ 0.95. For q ≳ 0.95, no apparent horizon is formed. The distribution of matter shows a central disk plus an expanding ring. It is found that electromagnetic-like field in the [(2+1)+1]-formalism plays an important role in a formation of a rotating black hole. Local conservation of angular momentum is checked. Accuracy of constraint equations is also shown to see the truncation error in the numerical calculations.

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