Motivated by the cosmological wormhole solutions obtained from our recent numerical investigations, we provide a definition of a wormhole which applies to dynamical situations. Our numerical solutions do not have timelike trapping horizons but they are wormholes in the sense that they connect two or more asymptotic regions. Although the null energy condition must be violated for static wormholes, we find that it can still be satisfied in the dynamical context. Two analytic solutions for a cosmological wormhole connecting two Friedmann universes without trapping horizons are presented.

We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an (n − 2)-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant. We assume that the Gauss-Bonnet coupling constant is non-negative. The quasi-local mass was recently defined by one of the authors as a counterpart of the Misner-Sharp quasi-local mass in general relativity. The quasi-local mass is found to be a quasi-local conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energy-balance law. In the asymptotically flat case, it converges to the Arnowitt-Deser-Misner mass at spacelike infinity, while it does to the Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS. Under the dominant energy condition, we show the monotonicity of the quasi-local mass for any k, while the positivity on an untrapped hypersurface with a regular center is shown for k = 1 and for k = 0 with an additional condition, where k = ±1, 0 is the constant sectional curvature of each spatial section of equipotential surfaces. Under a special relation between coupling constants, positivity of the quasi-local mass is shown for any k without assumptions above. We also classify all the vacuum solutions by utilizing the generalized Kodama vector. Lastly, several conjectures on further generalization of the quasi-local mass in Lovelock gravity are proposed.

We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in n(≥ 5) dimensions. The spacetimes are given as a warped product M 2 × K n−2 , where K n−2 is a (n − 2)-dimensional constant curvature space. We establish a generalized Birkhoff's theorem by showing that it is the unique electrically charged solution with this isometry and for which the orbit of the warp factor on K n−2 is non-null. An extension of the analysis for full Lovelock gravity is also achieved with a particular attention to the Chern-Simons case.

The hedgehog ansatz for spherically symmetric spacetimes in self-gravitating nonlinear sigma models and Skyrme models is revisited and its generalization for non-spherically symmetric spacetimes is proposed. The key idea behind our construction is that, even if the matter fields depend on the Killing coordinates in a nontrivial way, the corresponding energy-momentum tensor can still be compatible with spacetime symmetries. Our generalized hedgehog ansatz reduces the Skyrme equations to coupled differential equations for two scalar fields together with several constraint equations between them. Some particular field configurations satisfying those constraints are presented in several physically important spacetimes, including stationary and axisymmetric spacetimes. Incidentally, several new exact solutions are obtained under the standard hedgehog ansatz, one of which represents a global monopole inside a black hole with the Skyrme effect.