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A full four-dimensional calculation in which the radiation reshapes spacetime as it goes has not been done.","posed_since":"","precise":"Solve the semiclassical Einstein equations with the renormalized $\\langle T_{ab}\\rangle$ of $N_{f}$ free massless fields (all angular momenta, not only s-waves) for a black hole formed by collapse, from formation to $M \\sim m_{P}$, with $N_{f}$ large to suppress fluctuations. Determine the evolution of the apparent and event horizons, whether an inner apparent horizon forms and where the trapped region closes, and the deviation of $\\mathrm{d}M/\\mathrm{d}t$ from the adiabatic rate. An answer is a numerical or analytic spacetime with controlled errors.","problem_ref":null,"references":"","settled_by":"A convergent numerical solution of the 4D semiclassical equations through most of the evaporation with the full renormalized stress tensor.","status_note":"Fully back-reacted solutions exist in 2D dilaton models such as CGHS (Ashtekar, Pretorius, Ramazanoglu 2011); the 4D problem with the complete stress tensor is open as of 2026.","title":"Self-consistent evaporation of a 4D black hole including 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