Gravitation, local supersymmetry and higher spin fields: asymptotically flat structure in 3D and anisotropic scaling in higher odd dimensions.

Abstract

The idea that spacetime may have more than four dimensions has become a standard assumption in high energy physics. A natural extension of General Relativity in higher spacetime dimensions that requires the same basic principles, namely, general covariance, second-order equations for the metric and the conservation of stress-energy tensor, is known as Lovelock theory. This theory possesses additional coupling constants that are not xed from rst principles. Remarkably, in odd dimensions, for a precise tuning of these constants, the theory turns out to be equivalently described as a gauge theory with Chern-Simons action. It is in the context of Lovelock theory, that asymptotically Lifshitz wormholes and black holes in vacuum are shown to exist in d = 2n + 1 > 7 dimensions. The coupling constants are selected by requiring that all but one of their n maximally symmetric vacua are AdS spacetimes of radius l and degenerate. The asymptotic behaviour of these solutions is described by Lifshitz spacetimes with a dynamical exponent determined by a precise quotient of the curvature radii of the maximally symmetric vacua and the nondegenerate one. Besides, the asymptotically Lifshitz black hole possesses a xed Hawking temperature. Further analytic solutions, including pure Lifshitz spacetimes with a nontrivial geometry at the spacelike boundary, and wormholes that interpolate between asymptotically Lifshitz spacetimes with diferent dynamical exponents are also shown to exist.