Exotica or the failure of the strong cosmic censorship in four dimensions

Abstract

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 ${\mathbb{R}}^4$'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.

LaTeX, 11 pages, 1 figure, the final published version

References in corpus (2)

• Cosmic censorship of smooth structures
• A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory

Cited by in corpus (3)

• Global solvability of the vacuum Einstein equation and the strong cosmic censorship in four dimensions
• Exotica and the status of the strong cosmic censor conjecture in four dimensions
• Strong cosmic censorship and topology change in four dimensional gravity