  In this paper we discuss possible effects of non-locality in black hole
spacetimes. We consider a two-dimensional theory in which the action describing
matter is a ghost-free modification of the Polyakov action. For this purpose we
write the Polyakov action in a local form by using an auxiliary scalar field
and modify its kinetic term by including into it a non-local ghost-free form
factor. We demonstrate that the effective stress-energy tensor is modified and
we study its properties in a background of a two-dimensional black hole. We
obtain the expression for the contribution of the ghost-free auxiliary field to
the entropy of the black hole. We also demonstrate that if the back-reaction
effects are not taken into account, such a ghost-free modification of the
theory does not change the energy flux of the Hawking radiation measured at
infinity. We illustrate the discussed properties for black hole solution of a
2D dilaton gravity model which admits a rather complete analytical study.
