Evaporating dynamical horizon with the Hawking effect in Vaidya spacetime

We consider how the mass of the black hole decreases due to the Hawking radiation in the Vaidya spacetime, using the concept of the dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that the final state is the Minkowski spacetime in our particular model.

Figure 1

For the case that the dynamical horizon decreases, we should choose $l^a=-{\widehat{t}}^a+{\widehat{r}}^a$ so that $l^a$ points into the dynamical horizon.

Figure 2

Numerical calculation of the black hole mass $M$ as a function of $v$ from Eq. (38).