  We discuss how in certain theories of spacetime admitting a maximal proper
acceleration Hawking radiation does not completely evaporate the black hole.
The black hole remnant's mass depends on the inverse of the maximal
acceleration. Furthermore, as a consequence of a duality between the minimum
mass that a Schwarzschild black hole can have in such spacetimes and the
maximal acceleration, we show that in certain theories with a maximal
acceleration there must be an upper uniform bounds on the value of the force
that can be exerted on test particles.
