Model for nonsingular black hole collapse and evaporation

We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with the help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress energy preventing the formation of a singularity.

Figure 1

Penrose diagram of the regular static black hole solution with two asymptotically flat regions. Both horizons, located at $r_{+}$ and $r_{-}$, are marked in blue and red, respectively.

Figure 2

$G^r{}_v$ as a function of $r$ for radially ingoing radiation and $m^{\prime }(v)=1$. The solid line depicts the classical case for $ϵ$, $a_0\to 0$. The long-dashed line is for $m(v)=20$, ($r_{*}>\sqrt{a_0}$), and the short-dashed line is for $m(v)=5$, ($r_{*}<\sqrt{a_0}$). All quantities are in Planck units.

Figure 3

Penrose diagram for the formation and evaporation of the regular black hole metric. The red and dark blue solid lines depict the two trapping horizons $r_{-}$ and $r_{+}$. The brown dotted line is the curve of $r=\sqrt{a_0}$, and the black dashed one is $r_{*}$. The light blue arrows represent positive energy flux; the magenta arrows negative energy flux.