Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the field equations form an integrable system. The analysis of the critical points for this integrable model is the main subject of this work. To perform the analysis, we work on dimensionless variables that are different from those of the Hubble normalization. New critical points are derived, while the gravitational effects which follow from the cubic term are studied.

A class of generalized Galileon cosmological models, which can be described by a pointlike Lagrangian, is considered in order to utilize Noether’s theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Because of the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

We report the existence of unstable s-wave modes for black strings in Gauss-Bonnet theory (which is quadratic in the curvature) in seven dimensions. This theory admits analytic uniform black strings that are, in the transverse section, black holes of the same Gauss-Bonnet theory in six dimensions. All the components of the perturbation can be written in terms of a single component and its derivatives. For this, we find a master equation that admits bounded solutions provided the characteristic time of the exponential growth of the perturbation is related to the wave number along the extra direction, as in general relativity. It is known that these configurations suffer from a thermal instability; therefore, the results presented here provide evidence for the Gubser-Mitra conjecture in the context of Gauss-Bonnet theory. Because of the nontriviality of the curvature of the background, all of the components of the metric perturbation appear in the linearized equations. Similar to spherical black holes, the black strings should be obtained as the short-distance limit $r\ll {\alpha }^{1/2}$ of the black-string solution of Einstein-Gauss-Bonnet theory (which is not known analytically), where $\alpha$ is the Gauss-Bonnet coupling.

In the context of generalized Brans-Dicke cosmology we use the Killing tensors of the minisuperspace in order to determine the unspecified potential of a scalar-tensor gravity theory. Specifically, based on the existence of contact symmetries of the field equations, we find four types of potentials which provide exactly integrable dynamical systems. We investigate the dynamical properties of these potentials by using a critical point analysis and we find solutions which lead to cosmic acceleration and under specific conditions we can have de-Sitter points as stable late-time attractors.

In this paper an intrinsically non-Abelian black hole solution for the SU(2) Einstein-Yang-Mills theory in four dimensions is constructed. The gauge field of this solution has the form of a meron whereas the metric is the one of a Reissner-Nordstr\"om black hole in which, however, the coefficient of the $1/r^2$ term is not an integration constant. Even if the stress-energy tensor of the Yang-Mills field is spherically symmetric, the field strength of the Yang-Mills field itself is not. A remarkable consequence of this fact, which allows to distinguish the present solution from essentially Abelian configurations, is the Jackiw, Rebbi, Hasenfratz, 't Hooft mechanism according to which excitations of bosonic fields moving in the background of a gauge field with this characteristic behave as Fermionic degrees of freedom.Comment: LaTex, 17 pages, 1 figure. A detailed derivation of the Jackiv-Rebbi-Hasenfratz-t Hooft in this curved space-time has been added. Accepted for pubication in Phys. Lett.