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arXiv · 1908.09126

On the instability of some k-essence space-times

K. A. Bronnikov·J. C. Fabris·Denis C. Rodrigues
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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.

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K. A. Bronnikov, J. C. Fabris, Denis C. Rodrigues. 2019-08-24. On the instability of some k-essence space-times. https://doi.org/10.1142/s0218271820500169

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