Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
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时空的双曲切片：奇点避免和规范冲击
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发表时间：
2002
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通讯作者：
M. Alcubierre
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作者：
M. Alcubierre
我研究了博纳-马索族的双曲切片条件，特别是考虑了它在逼近两种不同类型的奇点时的性质：聚焦奇点和规范冲击。对于聚焦奇点，我扩展了Bona等人的原始分析，并证明了当偏差趋于零时，对于某些类型的切片条件的行为，可以获得边缘和强烈奇点避免。对于量规冲击的情况，我重新推导了以前发现的消除它们的条件。不幸的是，这种情况极大地限制了所允许的切片类型。然而，如果只要求大致满足这个条件，仍然可以找到有用的切片条件。这种限制较少的条件包括1+对数家族中的一个特定成员，在过去的经验中，这种家族对布里尔波和黑洞的模拟都是非常稳健的。
I study the Bona–Masso family of hyperbolic slicing conditions, considering in particular its properties when approaching two different types of singularities: focusing singularities and gauge shocks. For focusing singularities, I extend the original analysis of Bona et al and show that both marginal and strong singularity avoidance can be obtained for certain types of behaviour of the slicing condition as the lapse approaches zero. For the case of gauge shocks, I rederive a condition found previously that eliminates them. Unfortunately, such a condition limits considerably the type of slicings allowed. However, useful slicing conditions can still be found if one asks for this condition to be satisfied only approximately. Such less restrictive conditions include a particular member of the 1+log family, which in the past has been found empirically to be extremely robust for both Brill wave and black-hole simulations.