Numerical investigation into the interior of a spherically symmetric evaporating charged black hole

The solution to Einstein's equation describing rotating or charged black holes
(Kerr or ReissnerNordström solutions respectively) contains an inner horizon.
This inner horizon is also a Cauchy horizon, beyond which solutions to the eld
equations fail to be unique, therefore physical predictability breaks down there.
In the pure Kerr or ReissnerNordström solutions, the analytical extension of
the geometry beyond the inner horizon describes a smooth passage to other
external universes. However, quantum perturbations are expected to have a
signicant eect on the regularity of the inner horizon. In this research, we are
interested in the question of the inner horizon traversability, taking into account
these quantum eects. These quantum eects are studied in the framework of
semiclassical gravity, wherein the stress energy tensor inserted into Einstein's
equation is taken to be the renormalized expectation value of the stress energy
tensor of the quantum elds present in spacetime. We are here interested in
how does this quantum stress energy tensor deform the spacetime geometry, an
eect generally called backreaction. In this research we restrict our attention
to spherical symmetry, focusing on the case of spherically symmetric evaporating
charged black holes. An analytical approximation was developed by Amos
Ori and Noa Zilberman (and will be briey reviewed here). In this work we
seek to numerically check the validity of this analytical approximation. To this
end, we developed a numerical code which evolves Einstein's equation (with
the quantum stress-energy contribution added to it) for the evolving spherically
symmetric metric inside an evaporating semiclassical charged black hole. We
explore the results of running this numerical code in several representative cases,
and conrm the validity of the above mentioned analytical approximation in all
these cases.