Fossil Gravity - Supplement IX: Extremal Black Holes and the Third Law. Complementarity of Kehle / Unger (2026) and Fossil Gravity

AbstractKehle and Unger (2026, Phys. Rev. Lett.) prove numerically that the third law of black hole mechanics isviolated in five-dimensional vacuum gravity: an extremal rotating black hole — with vanishing surfacegravity κ = 0 — can form in finite time from a non-extremal precursor. This is the first example of sucha violation without a matter model. We show that this result is structurally complementary to fossilgravity theory. Supplement VIII derives that C_local → 0 as Hawking evaporation completes(Eq. VIII-21), describing the same extremal limit approached from the inside via evaporation.Kehle/Unger describe the same limit approached from the outside via accretion. The two paths areinverse processes in the fossil framework. We identify an open question for fossil gravity: the behaviourof the Zone ε phase boundary condition t_metric·t_C/t_P² = −1 in the extremal limit κ → 0, and whetherthe M² scaling of the Z_S term (Supplement VII, Eq. VII-29) remains well-defined at κ = 0. TheKehle/Unger result is in 5D; its extension to 4D remains open.