Obstructions to Minimal Regular Black Hole Cosmologies

Abstract

We derive an obstruction to FRW daughter cosmologies from static, asymptotically flat regular black holes. The trapped region of such a parent is Kantowski--Sachs rather than FRW, so the daughter must be introduced as a separate matched region. For closed daughters, the angular Darmois condition is controlled by the Misner--Sharp mass: asymptotic flatness and finite ADM mass force the induced density to decay as $A^{-3}$, while the $k=+1$ curvature term scales as $A^{-2}$. The minimal closed branch is therefore bounded rather than indefinitely expanding. Flat and open daughters avoid this boundedness mechanism, but the general flat/open FRW completeness theorem prevents non-static curvature-regular, ANEC-consistent flat/open daughters from being geodesically complete. For Bardeen, the parent source does not naturally supply the late-time support needed for an unbounded closed daughter. A viable FRW daughter therefore requires additional structure, such as modified asymptotics, nonminimal matching, non-FRW evolution, or an additional stress-energy component.