  We consider the Einstein-scalar-Gauss-Bonnet theory and assume that, at
regimes of large curvature, the Ricci scalar may be ignored compared to the
quadratic Gauss-Bonnet term. We then look for static, spherically-symmetric,
regular black-hole solutions with a non-trivial scalar field. Despite the use
of a general form of the spacetime line-element, no black-hole solutions are
found. In contrast, solutions that resemble irregular particle-like solutions
or completely regular gravitational solutions with a finite energy-momentum
tensor do emerge. In addition, in the presence of a cosmological constant,
solutions with a horizon also emerge, however, the latter corresponds to a
cosmological rather than to a black-hole horizon. It is found that, whereas the
Ricci term works towards the formation of the positively-curved topology of a
black-hole horizon, the Gauss-Bonnet term exerts a repulsive force that hinders
the formation of the black hole. Therefore, a pure scalar-Gauss-Bonnet theory
cannot sustain any black-hole solutions. However, it could give rise to
interesting cosmological or particle-like solutions where the Ricci scalar
plays a less fundamental role.
