  Dictated by the string theory and various higher dimensional scenarios, black
holes in $D>4$-dimensional space-times must have higher curvature corrections.
The first and dominant term is quadratic in curvature, and called the
Gauss-Bonnet (GB) term. We shall show that although the Gauss-Bonnet correction
changes black hole's geometry only softly, the emission of gravitons is
suppressed by many orders even at quite small values of the GB coupling. The
huge suppression of the graviton emission is due to the multiplication of the
two effects: the quick cooling of the black hole when one turns on the GB
coupling and the exponential decreasing of the grey-body factor of the tensor
type of gravitons at small and moderate energies. At higher $D$ the tensor
gravitons emission is dominant, so that the overall lifetime of black holes
with Gauss-Bonnet corrections is many orders larger than was expected. This
effect should be relevant for the future experiments at the Large Hadron
Collider (LHC). Keywords: Hawking radiation, black hole evaporation.
