相对论星系动力学定态的维里不等式
Virial inequalities for steady states in relativistic galactic dynamics
摘要：
众所周知，在非相对论星系动力学中广泛使用的Vlasov-Poisson系统的定态具有负能量。在本文中，我们得到了Vlasov-Poisson系统的两个相对论推广：Nordström-Vlasov系统和Einstein-Vlasov系统的类似性质。在第一种情况下，我们表明，稳定状态的能量是有界的总静止质量;在第二种情况下，我们也假设球对称，我们证明了一个不等式，其中不仅涉及能量和静止质量，但也中心红移。在这两种情况下的证明利用积分不等式满足的时间依赖的解决方案，并使用向量场乘子方法。
英文摘要：
It is well known that steady states of the Vlasov-Poisson system, a widely used model in non-relativistic galactic dynamics, have negative energy. In this paper we derive the analogous property for two relativistic generalizations of the Vlasov-Poisson system: The Nordström-Vlasov system and the Einstein-Vlasov system. In the first case we show that the energy of steady states is bounded by their total rest mass; in the second case, where we also assume spherical symmetry, we prove an inequality which involves not only the energy and the rest mass, but also the central redshift. In both cases the proof makes use of integral inequalities satisfied by time depedent solutions and which are derived using the vector fields multipliers method.
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