We present arguments for the existence of new black string solutions with negative cosmological constant. These higher-dimensional configurations have no dependence on the 'compact' extra dimension, and their conformal infinity is the product of time andThe configurations with an event horizon topology S d−2 × S 1 have a nontrivial, globally regular limit with zero event horizon radius. We discuss the general properties of such solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. Upon performing a dimensional reduction we prove that the reduced action has an effective SL(2, R) symmetry. This symmetry is used to construct non-trivial solutions of the Einstein-Maxwell-Dilaton system with a Liouville-type potential for the dilaton in (d − 1)-dimensions.

We construct new solutions of the vacuum Einstein field equations with cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. For a negative cosmological constant these solutions are N U T charged generalizations of the topological black hole solutions in higher dimensions. We also point out the existence of such N U T charged spacetimes in odd dimensions and we explicitly construct such spaces in 5 and 7 dimensions. The existence of such spacetimes with non-trivial topology is closely related to the existence of the cosmological constant. Finally, we discuss the global structure of such solutions and possible applications in string theory.

Higher dimensional, direct analogues of the usual d = 4 Einstein-Yang-Mills (EYM) systems are studied. These consist of the gravitational and Yang-Mills hierarchies in d = 4p dimensional spacetimes, both consisting of 2p-form curvature terms only. Regular and black hole solutions are constructed in 2p + 2 ≤ d ≤ 4p, in which dimensions the total mass-energy is finite, generalising the familiar BartnikMcKinnon solutions in EYM theory for p = 1. In d = 4p, this similarity is complete. In the special case of d = 2p + 1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d = 2p + 1 purely gravitational systems, whose solutions generalise the static d = 3 BTZ solutions, are discussed.

We construct new solutions of the vacuum Einstein field equations with multiple NUT parameters, with and without cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. We also find the the multiple nut parameter extension of the inhomogeneous Einstein metrics on complex line bundles found recently by Lü, Page and Pope. We also provide a more general form of the Eguchi-Hanson solitons found by Clarkson and Mann. We discuss the global structure of such solutions and possible applications in string theory.

We consider in more detail the covariant counterterm proposed by Mann and Marolf in asymptotically flat spacetimes. With an eye to specific practical computations using this counterterm, we present explicit expressions in general d dimensions that can be used in the so-called 'cylindrical cut-off' to compute the action and the associated conserved quantities for an asymptotically flat spacetime. As applications, we show how to compute the action and the conserved quantities for the NUT-charged spacetime and for the Kerr black hole in four dimensions.