  Scalar Gauss-Bonnet gravity is the only theory with quadratic curvature
corrections to general relativity whose field equations are of second
differential order. This theory allows for nonperturbative dynamical
corrections and is therefore one of the most compelling case studies for
beyond-general relativity effects in the strong-curvature regime. However,
having second-order field equations is not a guarantee for a healthy time
evolution in generic configurations. As a first step towards evolving
black-hole binaries in this theory, we here derive the 3+1 decomposition of the
field equations for any (not necessarily small) coupling constant and we
discuss potential challenges of its implementation.
