Stacking a 4D geometry into an Einstein-Gauss-Bonnet bulk

Abstract

In Einstein gravity there is a simple procedure to build D-dimensional spacetimes starting from (D-1)-dimensional ones, by stacking any (D-1)-dimensional Ricci-flat metric into the extra-dimension. We analyze this procedure in the context of Einstein-Gauss-Bonnet gravity, and find that it can only be applied to metrics with a constant Krestschmann scalar. For instance, we show that solutions of the black-string type are not allowed in this framework.

8 pages, no figures; some references added and other minor modifications to match the PRD accepted version

References in corpus (19)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• Modeling the fifth dimension with scalars and gravity
• Brane-World Black Holes
• General Gauss-Bonnet brane cosmology
• General Properties of the Self-tuning Domain Wall Approach to the Cosmological Constant Problem
• Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet theories
• Friedmann-Robertson-Walker brane cosmological equations from the five-dimensional bulk (A)dS black hole
• Supergravity on the Brane
• Braneworld Cosmology in (Anti)--de Sitter Einstein--Gauss--Bonnet--Maxwell Gravity
• Various Modified Solutions of the Randall-Sundrum Model with the Gauss-Bonnet Interaction
• Avoidance of Naked Singularities in Dilatonic Brane World Scenarios with a Gauss-Bonnet Term
• String inspired braneworld cosmology
• Effective Gauss-Bonnet Interaction in Randall-Sundrum Compactification
• Domain walls without cosmological constant in higher order gravity
• Brane World Cosmology with Gauss-Bonnet Interaction
• Brane localization of gravity in higher derivative theory
• Ricci-Flat Branes
• Embeddings in Non-Vacuum Spacetimes

Cited by in corpus (20)

• Brane-World Gravity
• Brane-world gravity
• Black Holes in Pure Lovelock Gravities
• Constraints on Gauss-Bonnet Gravity in Dark Energy Cosmologies
• Higher order gravity theories and their black hole solutions
• On black strings & branes in Lovelock gravity
• Obstructions on the horizon geometry from string theory corrections to Einstein gravity
• Matching conditions for a brane of arbitrary codimension
• Simple compactifications and Black p-branes in Gauss-Bonnet and Lovelock Theories
• Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem
• Five-dimensional black strings in Einstein-Gauss-Bonnet gravity
• Braneworld cosmological models with anisotropy
• Birkhoff's Theorem in Lovelock Gravity for General Base Manifolds
• Black Holes on Thin 3-branes of Codimension-2 and their Extension into the Bulk
• Instability of black strings in third-order Lovelock theory
• Lovelock Branes
• Embedding of two de-Sitter branes in a generalized Randall Sundrum scenario
• Einstein-Gauss-Bonnet black strings at large $\alpha$
• Effective actions of a Gauss-Bonnet brane world with brane curvature terms
• Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D