关于某些k-本质时空的不稳定性
On the instability of some k-essence space-times
摘要：
本文研究了k-本质理论中静态球对称位形的稳定性，其拉格朗日量的形式为$F(X)$，$X \equiv ϕ_{,α} ϕ^{,α}$ .证明了最近得到的两个精确解$F(X) =F_0 X^{1/3}$和$F(X) = F_0 X^{1/2} - 2 Λ$在球对称扰动下的不稳定性，其中$F_0$和$Λ$是常数.第一个解描述了渐近奇异时空中的一个黑洞，第二个解包含两个由虫洞连接的无限大视界。讨论了具有$n < 1/2$的球对称k-本质组态的一般不稳定性，因为扰动方程不是双曲型的。
英文摘要：
We study the stability properties of static, spherically symmetric configurations in k-essence theories with the Lagrangians of the form $F(X)$, $X \equiv ϕ_{,α} ϕ^{,α}$. The instability under spherically symmetric perturbations is proved for two recently obtained exact solutions for $F(X) =F_0 X^{1/3}$ and for $F(X) = F_0 X^{1/2} - 2 Λ$, where $F_0$ and $Λ$ are constants. The first solution describes a black hole in an asymptotically singular space-time, the second one contains two horizons of infinite area connected by a wormhole. It is argued that spherically symmetric k-essence configurations with $n < 1/2$ are generically unstable because the perturbation equation is not of hyperbolic type.
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