  In this note we classify a certain family of solutions of Lovelock gravity in
the Chern-Simons (CS) case, in arbitrary (odd) dimension greater than four. The
spacetime is characterized by admitting a metric that is a warped product of a
two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean base
manifold Sigma(d-2) of dimension d-2. We show that the solutions are naturally
classified in terms of the equations that restrict the base manifold. According
to the strength of such constraints we found the following branches in which
Sigma(d-2) has to fulfill: a Lovelock equation with a single vacuum (Euclidean
Lovelock Chern-Simons in dimension d-2), a single scalar equation that is the
trace of an Euclidean Lovelock CS equation in dimension d-2, or finally a
degenerate case in which the base manifold is not restricted at all. We show
that all the cases have some degeneracy in the sense that the metric functions
are not completely fixed by the field equations. This result extends the static
five-dimensional case previously discussed in Phys.Rev. D76 (2007) 064038, and
it shows that in the CS case, the inclusion of higher powers in the curvature
does not introduce new branches of solutions in Lovelock gravity. Finally we
comment on how the inclusion of a non-vanishing torsion and matter fields may
modify this analysis.

High Energy Physics - Theory;General Relativity and Quantum Cosmology