lies in p's past, the Turing machine can signal (a solution) to p at any stage of this never-ending task.
Meanwhile, the observer takes a quick trip (finite proper time) through spacetime to p, to pick up the solution.
As matter and radiation fall into a black hole, they are focused and blueshifted (their wavelengths become shorter) due to the intense gravitational field.
The blueshifted energy of the infalling radiation should, in principle, have a significant impact on the spacetime geometry near the inner horizon.
This instability is a challenge for the predictability of general relativity because it could potentially lead to a breakdown of the deterministic nature of the theory.
The mass inflation scenario is a product of classical general relativity and does not take into account quantum effects, which are expected to become significant in regions of such high curvature and energy density.
Quantum gravity is anticipated to provide a more complete and consistent description of what happens near and inside black holes, potentially resolving the issue of inner horizon instability and mass inflation.
(This, however, neglects the effects of black hole evaporation and the infinite blueshift that is encountered at the inner horizon.