We study the evaporation of a four-dimensional spherically symmetric black hole formed in a gravitational collapse. We analyze the back-reaction of a massless quantum scalar field conformally coupled to the scalar curvature by means of the semiclassical Einstein equations. We show that the evaporation is linked to an ingoing negative energy flux at the dynamical horizon and that this flux is induced by the quantum matter trace anomaly outside the black hole horizon whenever a suitable averaged energy condition is satisfied. For illustrative purposes, we evaluate the negative ingoing flux and the corresponding rate of evaporation in the case of a null radiating star described by the Vaidya spacetime.

我们研究了在引力坍缩中形成的四维球对称黑洞的蒸发。我们通过半经典爱因斯坦方程分析了与标量曲率共形耦合的无质量量子标量场的反向反应。我们表明，蒸发与动态视界处的传入负能量通量有关，并且只要满足合适的平均能量条件，该通量是由黑洞视界外的量子物质轨迹异常引起的。出于说明目的，我们评估了 Vaidya 时空描述的零辐射星情况下的负流入通量和相应的蒸发率。