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arXiv 2302.06346gr-qc
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广义Bianchi IX模型在宇宙奇点附近的动力学

The dynamics of general Bianchi IX model near the cosmological singularity

S. L. Parnovsky

摘要:

半个世纪前,别林斯基和哈拉特尼科夫基于比安奇IX型齐次模型的推广,提出了爱因斯坦方程在宇宙奇点附近的一般解。如果假设当接近奇点t=0时,它简化为所谓的渐近动力学,则对该模型的最一般的非对角情况的演化的考虑将大大简化,在该渐近动力学处不等式(6)成立。有人提出,从这个不等式第一次实现的那一刻起,直到时空的奇点,这个不等式一直是真的。我们分析了这一假设,并表明它是不正确的,在一般情况下。然而,它表明,总是有一个时间t_0,在此之后,这个假设成为真的。t_0值越小,模型的非对角化程度越小。Bianchi IX型的非对角齐次模型的行为的一些细节被认为是在渐近动力学的阶段接近奇点。

英文摘要:

Half a century ago, Belinsky and Khalatnikov proposed a generic solution of the Einstein equations near their cosmological singularity, based on a generalization of the homogeneous model of Bianchi type IX. Consideration of the evolution of the most general non-diagonal case of this model is greatly simplified if it is assumed that, when approaching the singularity t=0, it reduces to the so-called asymptotic dynamics, at which inequality (6) holds. It has been suggested that this inequality continues to be true from the moment of its first fulfilment up to the singularity of space-time. We analyze this assumption and show that it is incorrect in the general case. However, it is shown that there is always a time t_0, after which this assumption becomes true. The value of t_0 is the smaller the less is the degree of non-diagonality of the model. Some details of the behaviour of the non-diagonal homogeneous model of Bianchi type IX are considered at the stage of asymptotic dynamics of approaching the singularity.

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