Obstructions to Minimal Regular Black Hole Cosmologies

Abstract

We derive an obstruction to Friedmann--Lemaître--Robertson--Walker (FLRW) daughter cosmologies from static, asymptotically flat regular black holes. The trapped region of such a parent is Kantowski--Sachs rather than FLRW, 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. For their maximal homogeneous FLRW continuations, the regular-end affine-ANEC theorem excludes simultaneous non-staticity, curvature regularity, null geodesic completeness, and ANEC consistency. For Bardeen, the parent source does not naturally supply the late-time support needed for an unbounded closed daughter. Within these criteria, a viable FLRW daughter therefore requires additional structure, such as modified asymptotics, nonminimal matching, non-FLRW evolution, or an additional stress-energy component.

Version to appear in PRD; 25 pages, 1 figure