Numerical investigation of the interior geometry of semiclassical evaporating spherical charged black holes

We developed a numerical code which evolves the semiclassical Einstein's equation (with the quantum stress-energy contribution added as a source term) for the spherically symmetric metric inside an evaporating semiclassical charged black hole. An analytical approximation for the evolving semiclassical metric was recently developed by Ori and Zilberman (and will be briefly overviewed here). We seek to numerically check the validity of this analytical approximation. The Einstein equations in this case are partial differential equations for the two unknown metric functions which fully describe the spherically symmetric metric. We begin our numerical simulation close to the event horizon with regular initial data specified by a variant of the charged Vaidya metric. We then evolve the metric functions deep into the neighborhood of the inner horizon. We explore the results of running this numerical code in several representative cases. Our numerical simulations confirm the validity of the above mentioned analytical approximation in all these cases.