Renormings of Lp(Lq)L^p(L^q)

We investigate the best order of smoothness of $L^p(L^q)$. We prove in particular that there exists a $C^\infty$-smooth bump function on $L^p(L^q)$ if and only if $p$ and $q$ are both even integers and $p$ is a multiple of $q$.Comment: 18 pages; AMS-Te

Classical resolution of black hole singularities via wormholes

In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature.ns of curvature divergences in the context of space-time singularities.Comment: 6 pages, 4 figures; several improvements in main body and abstract; final version to appear in Eur. Phys. J.