标题： 视界形成与非轴对称空间中的环猜想 显示英文标题

标题： Apparent Horizon Formation and Hoop Conjecture in Non-axisymmetric Spaces

摘要： 我们通过数值研究检查了Thorne的环猜想在非轴对称时空中的有效性。 如果空间关于某一轴具有离散对称性，我们可以指定边界条件来确定非轴对称空间中的似地平线。 我们首次在具有离散对称性的非轴对称空间中实现了“环查找器”。 我们构建了在时间对称瞬间的渐近平坦真空解。 两种情况被检查：分布在环上的黑洞，以及分布在球面上的黑洞。 结果表明，计算${\cal C}$被简化为求解一个常微分方程。 我们发现，在非轴对称空间中，似地平线的存在与否与不等式${\cal C} \siml 4\pi M$一致。 显示英文摘要

摘要： 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: ${\cal C} \siml 4\pi M$.