On the instability of some k-essence space-times

TL;DR

This paper investigates the stability of static, spherically symmetric k-essence space-times, proving instability for specific solutions and discussing the general instability of configurations with certain kinetic term exponents.

Contribution

It provides a stability analysis of exact k-essence solutions, demonstrating their instability and discussing conditions for stability based on the kinetic term exponent.

Findings

Instability under spherically symmetric perturbations for specific solutions.

Black hole and wormhole solutions are unstable.

Configurations with kinetic exponent n < 1/2 are generally unstable.

Abstract

We study the stability properties of static, spherically symmetric configurations in k-essence theories with the Lagrangians of the form $F(X)$, $X \equiv \phi_{,\alpha} \phi^{,\alpha}$. The instability under spherically symmetric perturbations is proved for two recently obtained exact solutions for $F(X) =F_0 X^{1/3}$ and for $F(X) = F_0 X^{1/2} - 2 \Lambda$, where $F_0$ and $\Lambda$ 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.