The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued Euler characteristics of lower dimensions. The theory has many constant coefficients apparently without any physical meaning. However, it is possible, in a n...

In these lectures notes, we will discuss a particular higher order gravity theory, Lovelock theory, that generalises in higher dimensions than 4, general relativity. After briefly motivating modifications of gravity, we will introduce the theory in question and we will argue that it is a unique, mathematically sensible, and physically interesting extension of general relativity. We will see, by...

A theory of gravity in higher dimensions is considered. The usual Einstein-Hilbert action is supplemented with Lovelock terms, of higher order in the curvature tensor. These terms are important for the low energy action of string theories. The intersection of hypersurfaces is studied in the Lovelock theory. The study is restricted to hypersurfaces of co-dimension 1, (d− 1)-dimensional submanifo...

Black holes in several dimensions and in several theories are studied and discussed. The theories are, general relativity, Kaluza-Klein, Brans-Dicke, Lovelock gravity and string theory.

the asymptotically ads solutions of the einstein gravity with hyperbolic horizons in the presence of so(n(n-1)/2- 1,1) yang-mills fields governed by the non-abelian born-infeld lagrangian are presented. we investigate the properties of these solutions as well as their asymptotic behavior in various dimensions. the properties of these kinds of solutions are like the einstein-yang-mills solutions...

The situation of intersecting hypersurfaces in classical dimensionally continued Euler density gravity was introduced in our recent work [1]. We wish to simplify and demistify the calculations, providing an interesting geometrical interpretation. This analysis allows us to deal most efficiently with the division of space-time into a honeycomb network of cells which one might expect from membran...

Lovelock theory is a natural extension of Einstein theory of gravity to higher dimensions, and it is of great interest in theoretical physics as it describes a wide class of models. In particular, it describes string theory inspired ultraviolet corrections to Einstein-Hilbert action, while admits the Einstein general relativiy and the so called Chern-Simons theories of gravity as particular cas...