  We consider modifications to general relativity due to non-local string
effects by using perturbation theory about the 4-dimensional Schwarzschild
black hole metric. In keeping with our interpretation in previous works of
black holes as quantum p-branes we investigate non-local effects due to a
critical bosonic string compactified down to 4 dimensions. We show that
non-local effects do not alter the spacetime topology (at least
perturbatively), but they do lead to violations of the area law of black hole
thermodynamics and to Hawking's first law of black hole thermodynamics. We also
consider a simple analytic continuation of our perturbaive result into the
non-perturbative region, which yields an ultraviolet-finite theory of quantum
gravity. The Hawking temperature goes to zero in the non-perturbative region
(zero string tension parameter), which is consistent with the view that
Planck-size physics is quantum mechanical.
