Surprises in the Evaporation of 2D Black Holes

Quantum evaporation of Callan-Giddings-Harvey-Strominger black holes is analyzed in the mean-field approximation, incorporating backreaction. Detailed analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties (which are distinct from the features observed in the simplified, exactly soluble models). Finally, our results provide support for the full quantum gravity scenario recently developed by Ashtekar, Taveras, and Varadarajan.

Figure 1

A Penrose diagram of an evaporating CGHS black hole in the MFA. The incoming state is the vacuum on ${\mathcal{I}}_L^{-}$, and left-moving matter distribution on ${\mathcal{I}}_R^{-}$. The collapse creates a GDH, which subsequently evaporates. Quantum radiation fills the space-time to the causal future of matter. Inside the GDH, a singularity forms in the geometry. It meets the GDH when the latter shrinks to zero area. The last ray emanating from this meeting point is a future Cauchy horizon.

Figure 2

The final mass $m^{\star }$ versus the initial mass $M^{\star }$ (7) for a variety of initial data (8, 9). The curve fit to the data is $m^{\star }=\alpha (1-e^{-\beta (M^{\star }{)}^{\gamma }})$, with $\alpha \approx 0.864$, $\beta \approx 1.42$, and $\gamma \approx 1.15$.

Figure 3

$F^{\star }$ and $M_{\mathrm{Bondi}}^{\star }$ of Eq. (7) plotted against $y_{\mathrm{sh}}^{-}$ for solutions with several values of parameters $M^{\star }$ and $w$ of Eqs. (8, 9). In all cases, $F^{\star }$ starts at 0 in the distant past ($\kappa y_{\mathrm{sh}}^{-}\ll -1$) and then joins a universal curve at a time that depends on the initial mass. The time when the dynamical horizon first forms is marked on each flux curve.