We find large classes of non-asymptotically flat Einstein-Yang-MillsDilaton and Einstein-Yang-Mills-Born-Infeld-Dilaton black holes in N-dimensional spherically symmetric spacetime expressed in terms of the quasilocal mass. Extension of the dilatonic YM solution to N-dimensions has been possible by employing the generalized Wu-Yang ansatz. Another metric ansatz, which aided in finding exact solutions is the functional dependence of the radius function on the dilaton field. These classes of black holes are stable against linear radial perturbations. In the limit of vanishing dilaton we obtain Bertotti-Robinson type metrics with the topology of Ad S 2 ×S N −2 . Since connection can be established between dilaton and a scalar field of Brans-Dicke type we obtain black hole solutions also in the Brans-Dicke-Yang-Mills theory as well.

Recently in ( Phys. Rev. D 76, 087502 (2007) and Phys. Rev. D 77, 089903(E) (2008)) a thinshell wormhole has been introduced in 5-dimensional Einstein-Maxwell-Gauss-Bonnet (EMGB) gravity which was supported by normal matter. We wish to consider this solution and investigate its stability. Our analysis shows that for the Gauss-Bonnet (GB) parameter α < 0, stability regions form for a narrow band of finely-tuned mass and charge. For the case α > 0, we iterate once more that no stable, normal matter thin-shell wormhole exists.

We revisit the stability analysis of cylindrical thin-shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin-shell wormholes. The stability condition is summarized as the positivity of the second derivative of an effective potential at the equilibrium radius, i.e., V 00 ða 0 Þ > 0. This may serve as the master equation in all stability problems for the cylindrical thin-shell wormholes.

In D-dimensional spherically symmetric f (R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, isWe recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f (R) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples.