Black holes to white holes I. A complete quasi-classical model

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.