Instability of Reissner-Nordström black holes in de Sitter backgrounds

Recent numerical investigations have uncovered a surprising result: Reissner-Nordström-de Sitter black holes are unstable for spacetime dimensions larger than 6. Here we prove the existence of such instability analytically, and we compute the time scale in the near-extremal limit. We find very good agreement with the previous numerical results. Our results may be helpful in shedding some light on the nature of the instability.

Figure 1

Behavior of $V_{-}$ for different parameters, for $D=8$. Here we fix the event horizon at $r_b=1$, and the cosmological horizon at $r_c=1/0.95$. We consider $l=2$ modes and three different charges, $Q=0.2$, 0.35, 0.44.

Figure 2

The parametric region of instability in $Q/Q_{\mathrm{ext}}-r_b/r_c$ coordinates, according to criterium (14), for $l=2$. Top to bottom, $D=7$, 8, 9, 10, 11.