End Point of Hawking Evaporation -- Case of Integrable Model

Quantum back reaction due to $N$ massless fields may be worked out to a considerable detail in a variant of integrable dilaton gravity model in two dimensions. It is shown that there exists a critical mass of collapsing object of order $\hbar N \times$ (cosmological constant)$^{1/2}$, above which the end point of Hawking evaporation is two disconnected remnants of infinite extent, each separated by a mouth from the outside region. Deep inside the mouth there is a universal flux of radiation in all directions, in a form different from Hawking radiation. Below the critical mass no remnant is left behind, implying complete Hawking evaporation or even showing no sign of Hawking radiation. Existence of infinitely many static states of quantum nature is also demonstrated in this model.