論文

2018年

Uniqueness of static, isotropuc low-pressure solutions of the Einstein-Vlasov system

Proceedings of the 28th Workshop on General Relativity and Gravitation in Japan, JGRG 2018
  • Tomohiro Harada

3
開始ページ
33
終了ページ
34
記述言語
掲載種別
研究論文(国際会議プロシーディングス)

© Proceedings of the 28th Workshop on General Relativity and Gravitation in Japan, JGRG 2018. All rights reserved. The Vlasov matter reduces to a perfect fluid if the distribution function is isotropic in momentum space. A static solution of the Einstein-Vlasov system with isotropic distribution function is necessarily spherically symmetric and unique for a given surface potential provided that the pressure is sufficiently low and the energy cutoff of the distribution function is not too smooth. For a shallow potential and isotropic distribution function F(E) with F = 0 for E > E0 and F ≃ C(E0 − E)n near the cutoff E0, the EOS becomes polytropic. The uniqueness holds for 0 ≤ n < 7/2. We analytically and numerically investigated the case of a step-function distribution. There exists a unique spherically symmetric static solution for a shallow potential, while the uniquness may break down if the regime of a deep potential is included.

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