Quasinormal modes and a new instability of Einstein-Gauss-Bonnet black holes in the de Sitter world

Analysis of time-domain profiles for gravitational perturbations shows that Gauss-Bonnet black holes in a de Sitter world possess a new kind of dynamical instability which does not take place for asymptotically flat Einstein-Gauss-Bonnet black holes. The new instability is in the gravitational perturbations of the scalar type and is due to the nonvanishing cosmological constant. Analysis of the quasinormal spectrum in the stability sector shows that although the scalar type of gravitational perturbations alone does not obey Hod’s conjectural bound, connecting the damping rate and the Hawking temperature, the vector and tensor types (and thereby the gravitational spectrum as a whole) do obey it.

Figure 1

Nonoscillatory temporal profiles for scalar perturbations for $\alpha =0.5r_H^2$. The stable (red) and unstable (blue) profiles correspond to $\mathrm{\Lambda }=0.8/r_H^2$ and $\mathrm{\Lambda }=0.9/r_H^2$.

Figure 2

Stability and instability regions for tensor-type gravitational perturbations in ($D=6$)-dimensional Gauss-Bonnet–de Sitter spacetimes. This is the eikonal instability with the $\ell =\infty$ most unstable mode.

Figure 3

Stability and instability regions for scalar-type gravitational perturbations in $D=6$, $D=7$, and $D=8$ (from left to right).

Figure 4

Stability and instability regions for scalar-type gravitational perturbations in five dimensions. Upper right corner correspond to the $\mathrm{\Lambda }$ instability, while the lower right corner corresponds to the eikonal instability. The overlap of regions of both types of instability produce the instability region for $D=5$ case.

Figure 5

Stability and instability regions for gravitational perturbations in $D=6$ as overlap of the $\mathrm{\Lambda }$ instability in the scalar channel and eikonal instability in the tensor channel.

Figure 6

Scalar type of gravitational perturbations: Critical value of $\alpha$, corresponding to the threshold of instability as function of $r_H/r_C$ in dimensions six, seven, and eight.

Figure 7

Variation of the real (left panel) and imaginary (right panel) parts of the dominant quasinormal mode as functions of $r_H/r_C$ for scalar-type perturbations in five dimensions.

Figure 8

Variation of the imaginary part of the dominant quasinormal mode with respect to $r_H/r_C$ for vector- and tensor-type perturbations in five dimensions for $\alpha =0.2r_H^2$.