SELF-SIMILAR PERTURBATIONS OF A KANTOWSKI-SACHS MODEL

被引:6
作者
CARR, BJ
KOUTRAS, A
机构
[1] Astronomy Unit, School of Mathematical Sciences, Queen Mary and Westfield College, London E1 4NS, Mile End Road
关键词
COSMOLOGY; THEORY;
D O I
10.1086/172340
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We show that the spherically symmetric self-similar Einstein equations for a perfect fluid with equation of state p = alphamu permit a self-similar Kantowski-Sachs solution. For positive pressure (alpha > 0), the metric in this solution may be nonphysical and even complex. In particular, the alpha = 1/3 case corresponds to a tachyonic fluid with negative mass. For negative pressure (alpha < 0), as might be relevant for phase transitions in the early universe or if there is bulk viscosity, the solution is more physical and reduces to the Kantowski-Sachs solution found earlier by Wesson. We demonstrate that for each alpha there is a one-parameter family of spherically symmetric solutions which are asymptotic to the Kantowski-Sachs model at large or small distances. In the alpha > 0 case some of the solutions pass through a sonic point, and all of these have infinite pressure gradient there. In the alpha < 0 case there is no sonic point, and our solutions generalize the self-similar family found by Ponce de Leon. We examine the alpha = 1/3 and alpha = -1/2 solutions numerically.
引用
收藏
页码:34 / 50
页数:17
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