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arXiv 1506.01271gr-qc
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旋转宇宙学的初始数据

Initial data for rotating cosmologies

Piotr Bizoń, Stefan Pletka, Walter Simon

摘要:

利用共形方法重新讨论了具有正宇宙学常数的真空紧致流形上最大初始数据的构造。我们讨论、推广和应用Hebey等人[19]和Premoselli [31]的最新结果,这些结果给出了Lichnerowicz方程解的存在性、不存在性、(非)唯一性和(线性化)稳定性,取决于其系数。然后,我们专注于所谓的$(t,φ)$ -对称数据作为“种子流形”,特别是鲍文约克数据的圆形超环面$\mathbb{S}^2 \times \mathbb{S}$(一片纳里埃)和克尔deSitter。在前一种情况下,我们澄清的Lichnerowicz方程的轴对称解的分支结构的角动量作为分支参数,使用分析和数值技术相结合。至于后一个例子,我们展示了如何动态数据可以构建在一个自然的方式,通过共形重标度的克尔deSitter数据。

英文摘要:

We revisit the construction of maximal initial data on compact manifolds in vacuum with positive cosmological constant via the conformal method. We discuss, extend and apply recent results of Hebey et al. [19] and Premoselli [31] which yield existence, non-existence, (non-)uniqueness and (linearisation-) stability of solutions of the Lichnerowicz equation, depending on its coefficients. We then focus on so-called $(t,φ)$-symmetric data as "seed manifolds", and in particular on Bowen-York data on the round hypertorus $\mathbb{S}^2 \times \mathbb{S}$ (a slice of Nariai) and on Kerr-deSitter. In the former case, we clarify the bifurcation structure of the axially symmetric solutions of the Lichnerowicz equation in terms of the angular momentum as bifurcation parameter, using a combination of analytical and numerical techniques. As to the latter example, we show how dynamical data can be constructed in a natural way via conformal rescalings of Kerr-deSitter data.

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