Abstract

In Einstein’s theory of General Relativity (GR), gravity is described in terms of curvature of the spacetime, a four-dimensional Pseudo-Riemannian manifold. The field equations, which relate the curvature of spacetime and its matter content, form a system of quasilinear second-order PDEs in the metric. Interestingly, Lovelock showed that GR is the unique geometric theory of gravity that we can write down in four dimensions, such that the field equations are second order and energy is locally conserved. However, this ‘uniqueness’ does not persist in higher dimensions. In fact there exist more general theories satisfying these assumptions, the so-called Lovelock theories of gravity. These theories differ from GR in that their field equations are fully non-linear and these non-linearities give rise to several interesting phenomena which don’t appear in GR, such as superluminal propagation of signals or formation of shocks. I will discuss some general properties of Lovelock theories, their causal structure and the (im)possibility of constructing time machines.