Kiselev Black Holes in Anti-de Sitter Spacetime Are Not Viable

TL;DR

Problem: assess viability of Kiselev black holes in anti-de Sitter spacetime as local descriptions of black holes embedded in anisotropic dark energy. Approach: analyze the Euclidean brane action for the four-dimensional Kiselev-AdS metric and extract stability from the sign of the function $\\mathcal{F}(r)$, invoking Seiberg-Witten instability. Findings: stability requires $w \ge -1/3$ (i.e., $\\varepsilon \ge 2$), which conflicts with the dark-energy range $w < -1/3$, indicating the Kiselev-AdS background is unstable; numerical considerations reinforce the unbounded brane action for representative parameters. Significance: this excludes the Kiselev-AdS ansatz as a viable embedding for locally anisotropic dark energy in AdS and highlights a tension between dark-energy phenomenology and holographic stability, aligning with swampland-type constraints on gravity solutions.

Abstract

While the Kiselev black hole solution does not describe a perfect fluid quintessence, it is possible that dark energy fluid is not isotropic, and so one may hope that the solution may still describe at least locally a black hole embedded in such a dark energy fluid environment. Taking into account that the accelerated expansion of the Universe is caused by a dynamical dark energy fluid, and the actual underlying cosmological constant is negative as has been sometimes suggested, we show that the Kiselev solution is untenable as it is unstable against brane nucleation instability.

Figures (2)

• Figure 1: The normalized brane action, $\mathcal{F}(r)=\mathfrak{S}^\text{E}/8\pi^2 P L$, for Kiselev-AdS black hole with $K=L=1,M=10,\varepsilon=0.003$. The action is not bounded from below.
• Figure 2: The normalized brane action for Kiselev-AdS black hole, $\mathcal{F}(r)=\mathfrak{S}^\text{E}/8\pi^2 P L$, with $K=1,L=100,M=10,\varepsilon=1.5$. The action is not bounded from below.