On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System |
| |
Authors: | Håkan Andréasson |
| |
Institution: | 1.Mathematical Sciences,Chalmers and G?teborg University,G?teborg,Sweden |
| |
Abstract: | In a previous work 1] matter models such that the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1, were considered in the context of Buchdahl’s inequality. It was proved that static shell solutions of the spherically
symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, R
0, R
1], R
0 > 0, satisfies R
1/R
0 < 1/4. Moreover, given a sequence of solutions such that R
1/R
0 → 1, then the limit supremum of 2M/R
1 was shown to be bounded by ((2Ω + 1)2 − 1)/(2Ω + 1)2. In this paper we show that the hypothesis that R
1/R
0 → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov
system with this property. We also prove that for this sequence not only the limit supremum of 2M/R
1 is bounded, but that the limit is ((2Ω + 1)2 − 1)/(2Ω + 1)2 = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R
1 arbitrary close to 8/9, which is interesting in view of 3], where numerical evidence is presented that 8/9 is an upper bound
of 2M/R
1 of any static solution of the spherically symmetric Einstein-Vlasov system. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|