Backreaction due to quantum tunneling and modification to the black hole evaporation process

Hawking’s original approach [1] of black hole radiation is based on a global set up of collapsing geometry where the asymptotic in vacuum state is realized as a particle state in the asymptotic out vacuum. Such an evolution is believed to be non-unitary in the sense that a pure initial state evolves as a mixed state in the out region. In the late time limit when the black hole settles down one obtains a thermal (blackbody) radiation spectrum. While this picture is technically rigorous it does not consider the evaporation of black holes by incorporating the backreaction of the particles (on the spacetime and vice-versa) that are being emitted. Therefore one lacks a physical picture where the energy-momentum of the combined system is conserved. In order to do that one should see the eect of