ar X iv : 1 50 3 . 04 94 5 v 4 [ gr - q c ] 6 O ct 2 01 5 Exotica or the failure of the strong cosmic censorship in four dimensions

In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely—taking into account that the conjecture lacks any precise formulation yet—first we make sense of what one would mean by a “generic counterexample” by introducing the mathematically unambigous and logically stronger concept of a “robust counterexample”. Then making use of Penrose’ nonlinear graviton construction (i.e., twistor theory) and a Wick rotation trick we construct a smooth Ricci-flat but not flat Lorentzian metric on the largest member of the Gompf–Taubes uncountable radial family of large exotic R4’s. We observe that this solution of the Lorentzian vacuum Einstein’s equations with vanishing cosmological constant provides us with a sort of counterexample which is weaker than a “robust counterexample” but still reasonable to consider as a “generic counterexample”. It is interesting that this kind of counterexample exists only in four dimensions. AMS Classification: Primary: 83C75, Secondary: 57N13, 53C28