  We show that four-dimensional black holes become stable below certain mass
when the Einstein-Hilbert action is supplemented with higher-curvature terms.
We prove this to be the case for an infinite family of ghost-free theories
involving terms of arbitrarily high order in curvature. The new black holes,
which are non-hairy generalizations of Schwarzschild's solution, present a
universal thermodynamic behavior for general values of the higher-order
couplings. In particular, small black holes have infinite lifetimes. When the
evaporation process makes the semiclassical approximation break down (something
that occurs after a time which is usually infinite for all practical purposes),
the resulting object retains a huge entropy, in stark contrast with
Schwarzschild's case.
