A Model of Black Hole Evaporation and 4D Weyl Anomaly

Abstract

We analyze time evolution of a spherically-symmetric collapsing matter from a point of view that black holes evaporate by nature. We consider conformal matters and solve the semi-classical Einstein equation $G_{\mu\nu}=8\pi G \langle T_{\mu\nu} \rangle$ by using the 4-dimensional Weyl anomaly with a large $c$ coefficient. Here $\langle T_{\mu\nu} \rangle$ contains the contribution from both the collapsing matter and Hawking radiation. The solution indicates that the collapsing matter forms a dense object and evaporates without horizon or singularity, and it has a surface but looks like an ordinary black hole from the outside. Any object we recognize as a black hole should be such an object.