In this paper we, first, generalize the quasilocal definition of the stress energy tensor of Einstein gravity to the case of Lovelock gravity, by introducing the tensorial form of surface terms that make the action well-defined. We also introduce the boundary counterterm that removes the divergences of the action and the conserved quantities of the solutions of Lovelock gravity with flat boundary at constant t and r. Second, we obtain the metric of spacetimes generated by brane sources in dimensionally continued gravity through the use of Hamiltonian formalism, and show that these solutions have no curvature singularity and no horizons, but have conic singularity. We show that these asymptotically AdS spacetimes which contain two fundamental constants are complete.Finally we compute the conserved quantities of these solutions through the use of the counterterm method introduced in the first part of the paper. * email address: mhd@shirazu.ac.ir

We present the topological solutions of Einstein gravity in the presence of a non-Abelian YangMills field. In (n+1) dimensions, we consider the So(n(n−1)/2−1, 1) semisimple group as the YangMills gauge group, and introduce the black hole solutions with hyperbolic horizon. We argue that the 4-dimensional solution is exactly the same as the 4-dimensional solution of Einstein-Maxwell gravity, while the higher-dimensional solutions are new. We investigate the properties of the higherdimensional solutions and find that these solutions in 5 dimensions have the same properties as the topological 5-dimensional solution of Einstein-Maxwell (EM) theory although the metric function in 5 dimensions is different. But in 6 and higher dimensions, the topological solutions of EYM and EM gravities with non-negative mass have different properties. First, the singularity of EYM solution does not present a naked singularity and is spacelike, while the singularity of topological Reissner-Nordstrom solution is timelike. Second, there are no extreme 6 or higher-dimensional black holes in EYM gravity with non-negative mass, while these kinds of solutions exist in EM gravity.

Considering both the nonlinear invariant terms constructed by the electromagnetic field and the Riemann tensor in gravity action, we obtain a new class of (n + 1)-dimensional magnetic brane solutions in third order Lovelock-Born-Infeld gravity. This class of solutions yields a spacetime with a longitudinal nonlinear magnetic field generated by a static source. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle δ. We find that, as the Born-Infeld parameter decreases, which is a measure of the increase of the nonlinearity of the electromagnetic field, the deficit angle increases. We generalize this class of solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. We found that the conserved quantities do not depend on the Born-Infeld parameter, which is evident from the fact that the effects of the nonlinearity of the electromagnetic fields on the boundary at infinity are wiped away. We also find that the properties of our solution, such as deficit angle, are independent of Lovelock coefficients. * email address: mhd@shirazu.ac.ir †

We obtain two new classes of magnetic brane solutions in third order Lovelock gravity. The first class of solutions yields an (n + 1)-dimensional spacetime with a longitudinal magnetic field generated by a static source. We generalize this class of solutions to the case of spinning magnetic branes with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning brane, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters, while the static brane has no net electric charge. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Although the second class of solutions may be made electrically charged by a boost transformation, the transformed solutions do not present new spacetimes. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. * email address: mhd@shirazu.ac.ir