Scalar brane backgrounds in higher order curvature gravity

Abstract

We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general Lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularily emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Generically, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element.

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

“…Its coefficients are fixed by the reductioñ 29) and related to the curvature κ of the dilatonic black hole. We again concentrate on the Einstein branch of the solution.…”

Five-dimensional black strings in Einstein-Gauss-Bonnet gravity

“…(Though they have focused on a fourdimensional case, it does not contradict the above remark since in these works a scalar field coupled dilatonically to the Gauss-Bonnet term is introduced.) Very recently the Gauss-Bonnet correction is frequently discussed in the braneworld context as an attempt to extend the Randall-Sundrum model in a natural way [21,22]. Five-dimensional, static and spherically symmetric black holes were systematically examined in the presence of a Gauss-Bonnet term [23,24,25,26], and its consequences on the brane cosmology were discussed [26,27,28].…”

Dilaton Brane Cosmology With Second Order String Corrections and the Cosmological Constant

“…So, in order to explore the results from this point of view and ignoring any gauge field contributions for simplicity, we must have ( [31], [32], [34])…”