  This is the first of two papers presenting different versions of
quasi-classical toy models for the non-singular evolution of the geometry and
the associated effective stress-energy tensor for a spherically symmetric black
hole that evolves into a white hole and eventually disappears after evaporating
down to the Planck scale. The ansatz for the geometry is inspired by
calculations of the semi-classical stress-energy tensor in the Schwarzschild
background and ideas from loop quantum gravity for a nonsingular transition to
the white hole. In this paper the main emphasis is on the evolution of the
black hole, and the evolution of the white hole is assumed to be essentially
the time reverse of that of the black hole. The negative energy of the Hawking
"partners" flows out of the white hole to future null infinity. The white hole
disappears when the matter and radiation that collapsed to form the black hole
emerges. I discuss the compatibility of the model with some of the quantum
energy conditions proposed in the literature, and, briefly, the implications
for the interpretation of black hole entropy. The second paper considers how
the evolution of the white hole can be modified to avoid prolonged emission of
negative energy.
