Black holes and wormholes in higher-curvature corrected theories of gravity
We perform a thorough analysis of gravitational quasinormal spectrum of asymptotically de Sitter black holes in Einstein-Gauss-Bonnet theory. Usage of the time-domain integration allowed us to take into consideration contributions of all the modes in the signal and, thereby, to judge about the (in)stability of the black hole. Analysis of time-domain profiles for gravitational perturbations shows that black holes 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. We show that the quasinormal frequencies of the scalar type of gravitational perturbations do not obey Hod's inequality, however, the other two channels, vector and tensor, have lower-lying modes what, thereby, confirm Hod's proposal.
In the publication of P. Kanti, B. Kleihaus, J. Kunz, [Phys. Rev. Lett. 107, 271101 (2011)] it was shown that the four-dimensional Einstein-dilaton-Gauss-Bonnet theory allows for wormholes without introducing any exotic matter. The numerical solution for the wormhole was obtained there and it was claimed that this solution is gravitationally stable against radial perturbations, what, by now, would mean the only known theoretical possibility for the existence of an apparently stable, four-dimensional and asymptotically flat wormhole without exotic matter. Here, a more detailed analysis of perturbations shows that the Kanti-Kleihaus-Kunz wormhole is unstable against small perturbations for any values of its parameters. The exponential growth appears in the time domain after a long period of damped oscillations, in the same way as it takes place in the case of unstable higher-dimensional black holes in the Einstein-Gauss-Bonnet theory. The instability is driven by the purely imaginary mode, which is nonperturbative in the Gauss-Bonnet coupling $\alpha$.