Instability of some k-essence spacetimes

Abstract

We study the stability properties of static, spherically symmetric configurations in k-essence theories with the Lagrangians of the form F (X), X ≡ 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 −2Λ , 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.

The simplest wormhole in Rastall and k-essence theories

“…(84). Hence, unlike the Rastall case, the k-essence perturbation analysis is consistent, quite similarly to the results of [17,18].…”

“…If n < 1/2, Eq. (89) loses its hyperbolic nature, and the system is hydrodynamically unstable for the same reason as described in [17] and other papers.…”

“…The solutions turned out to be quite exotic, mainly due to the asymptotic properties at infinity. A stability analysis has shown that those k-essence solutions were unstable [17]. However, surprisingly, the perturbation analysis of the Rastall solutions was shown to be inconsistent, and the stability issue remained unclear [18].…”

Rastall's theory of gravity: Spherically symmetric solutions and the stability problem

“…[7]. The perturbation analysis of the k-essence solutions was carried out in [8], and it was concluded that they are unstable. Hence, it was natural to perform a similar analysis for the corresponding Rastall solutions since the equivalence with the k-essence solutions may not be preserved at the perturbative level.…”

“…In Ref. [8] the stability of the corresponding k-essence solutions under spherically symmetric perturbations was analyzed, and their instabilities have been proved. In the present paper, we undertake a similar analysis for the Rastall black hole-type solutions.…”