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Roman Konoplya (RUDN University),
" Two etudes on wormholes"
We shall present two recent papers devoted to perturbations and quasinormal spectra of wormholes.
Etude 1 (https://arxiv.org/pdf/1804.11170.pdf): In [P. Kanti, et. al. PRL 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 existence of an apparently stable, four dimensional and asymptotically flat wormhole without exotic matter. Here, 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 appear in 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.
Etude 2 (https://arxiv.org/pdf/1805.04718.pdf): Here we shall show how to reconstruct the shape function of a spherically symmetric traversable Lorenzian wormhole near its throat if one knows high frequency quasinormal modes of the wormhole. The wormhole spacetime is given by the Morris-Thorne ansatz. The solution to the inverse problem via fitting of the parameters within the WKB approach is unique for arbitrary tideless wormholes and some wormholes with non-zero tidal effects, but this is not so for arbitrary wormholes. As examples, we reproduce the near throat geometries of the Bronnikov-Ellis and tideless Morris-Thorne metrics by their quasinormal modes at high multipole numbers.