Radouane Gannouji, M. Sami
We derive field equations of Gauss-Bonnet gravity in 4 dimensions after
dimensional reduction of the action and demonstrate that in this scenario
Vainshtein mechanism operates in the flat spherically symmetric background. We
show that inside this Vainshtein sphere the fifth force is negligibly small
compared to the gravitational force. We also investigate stability of the
spherically symmetric solution, clarify the vocabulary used in the literature
about the hyperbolicity of the equation and the ghost-Laplacian stability
conditions. We find superluminal behavior of the perturbation of the field in
the radial direction. However, because of the presence of the non linear terms,
the structure of the space-time is modified and as a result the field does not
propagate in the Minkowski metric but rather in an "aether" composed by the
scalar field $\pi(r)$. We thereby demonstrate that the superluminal behavior
does not create time paradoxes thank to the absence of Causal Closed Curves. We
also derive the stability conditions for Friedmann Universe in context with
scalar and tensor perturbations.
View original:
http://arxiv.org/abs/1107.1892
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