Assuming an Einstein-Gauss-Bonnet theory of gravitation in a (D ≥ 5)-dimensional spacetime with boundary, we consider the problem of the boundary dynamics given the matter Lagrangian on it. The resulting equation is applied in particular on the derivation of the Friedmann equation of a 3-brane, understood as the non-orientable boundary of a 5d spacetime. We briefly discuss the contradictory conclusions of the literature.

We investigate some properties of n(≥ 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n − 2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C 2 vacuum solutions are classified into four types: (i) Schwarzschild-Tangherlinitype solution; (ii) Nariai-type solution; (iii) special degenerate vacuum solution; (iv) exceptional vacuum solution. The conditions for the realization of the last two solutions are clarified. The Schwarzschild-Tangherlini-type solution is studied in detail. We prove the first law of black-hole thermodynamics and present the expressions for the heat capacity and the free energy.

The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with cosmological constant, the gravitational sector contains the Lorentz-Chern-Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern-Simons theory for the supersymmetric extension of the Poincare and AdS groups, respectively. Here we introduce a duality map between different gravity theories that greatly simplifies the construction. This map relies on the different ways to make geometry emerge from a single gauge potential. The extension for N = p + q gravitini is also performed. *

Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are also equations relating the geometry of the shell (jump and average of the extrinsic curvature as well as the intrinsic curvature) to the non-singular components of the bulk stress tensor on the sides of the thin shell.The equations are applied to spherically symmetric thin shells in vacuum. The shells are part of the vacuum, they carry no energy tensor. We classify these solutions of 'thin shells of nothingness' in the pure Gauss-Bonnet theory. There are three types of solutions, with one, zero or two asymptotic regions respectively. The third kind of solution are wormholes. Although vacuum solutions, they have the appearance of mass in the asymptotic regions. It is striking that in this theory, exotic matter is not needed in order for wormholes to exist-they can exist even with no matter.

Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on the junction surface vanishes. So a spherical vacuum shell, containing no matter, arises as a boundary between two regions of the space-time. A general analysis is given of solutions that can be constructed by this method of geometric surgery. Such solutions are a generalized kind of spherically symmetric empty space solutions, described by metric functions of the class C 0 . New global structures arise with surprising features. In particular, we show that vacuum spherically symmetric wormholes do exist in this theory. These can be regarded as gravitational solitons, which connect two asymptotically ͑anti-͒de Sitter spaces with different masses and/or different effective cosmological constants. We prove the existence of both static and dynamical solutions and discuss their ͑in͒stability under perturbations that preserve the symmetry. This leads us to discuss a new type of instability that arises in five-dimensional Lovelock theory of gravity for certain values of the coupling of the Gauss-Bonnet term. The issues of existence and uniqueness of solutions and determinism in the dynamical evolution are also discussed.