Apparent Horizon Formation and Hoop Conjecture in Non-axisymmetric Spaces

Details Apparent Horizon Formation and Hoop Conjecture in Non-axisymmetric Spaces Apparent Horizon Formation and Hoop Conjecture in Non-axisymmetric Spaces

1999-04-21

arxiv.org/abs/gr-qc/9904054v2

Phys.Rev. D60 (1999) 044003; Erratum-ibid. D60 (1999) 089902

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, typos fixed, to be published in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.60.089902

We investigate the validity of Thorne's hoop conjecture in non-axisymmetric spacetimes by examining the formation of apparent horizons numerically. If spaces have a discrete symmetry about one axis, we can specify the boundary conditions to determine an apparent horizon even in non-axisymmetric spaces. We implement, for the first time, the ``hoop finder'' in non-axisymmetric spaces with a discrete symmetry. We construct asymptotically flat vacuum solutions at a moment of time symmetry. Two cases are examined: black holes distributed on a ring, and black holes on a spherical surface. It turns out that calculating ${\cal C}$ is reduced to solving an ordinary differential equation. We find that even in non-axisymmetric spaces the existence or nonexistence of an apparent horizon is consistent with the inequality: ${\cal C} \siml 4\pi M$.

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