Gravitational collapse of quantum matter

We describe a class of exactly soluble semiclassical models for gravitational collapse obtained by patching dynamical spherically symmetric exterior space-times with cosmological interior space-times. These are generalizations of the Oppenheimer-Snyder type models to include classical and quantum scalar fields as sources for the interior metric, and null fluids with pressure as sources for the exterior metric. The polymer quantization method is used for the scalar field. The resulting semiclassical metrics exhibit novel features such as evaporating horizons and singularity avoidance.

Figure 1

$k=1$ exterior with classical scalar field interior: the exterior space-time is dynamical and has null singularity at a fixed value of advanced time (here $v_0\sim 0.67$).

Figure 2

$k=2$ exterior with classical scalar field interior: the only solution is a static exterior [constant $m(v)$ and $g(v)$]. This is qualitatively similar to the Oppenheimer–Snyder solution.

Figure 3

$k=3$ exterior with classical scalar field interior: the exterior space-time is dynamical and has a null singularity at a value of advanced time (here, $v_0\sim 0.67$). The apparent horizon extends to spatial infinity.

Figure 4

$k=2$ exterior with quantum scalar field interior: the shell trajectory exponentially approaches $r=0$ and there is no curvature singularity. The apparent horizon forms and evaporates in finite time.