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

In this paper, 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.

Palatial twistor theory and the twistor googly problem

A key obstruction to the twistor programme has been its so-called ‘googly problem’, unresolved for nearly 40 years, which asks for a twistor description of right -handed interacting massless fields (positive helicity), using the same twistor conventions that give rise to left -handed fields (negative helicity) in the standard ‘nonlinear graviton’ and Ward constructions. An explicit proposal for resolving this obstruction— palatial twistor theory —is put forward (illustrated in the case of gravitation). This incorporates the concept of a non-commutative holomorphic quantized twistor ‘Heisenberg algebra’, extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation.

NONLINEAR GRAVITON AND THE PROBLEM OF MASS GENERATION

We argue that the massless mediator of a long range interaction can acquire mass through collision with a nonlinear graviton. The process displays analogy with the Higgs mechanism, and compensates for a broken mirror symmetry (duality), at the past–future bifurcation. Mass is formulated as the electric charge of a suitable state emerging from the particle–antiparticle (self–antiself dual) confrontation. Such considerations suggest that the experimental quest of the Higgs boson could in fact shed light on the (so far theoretical) quantum gravity programme.

NONLINEAR GRAVITON AS A LIMIT OF sl(N;C) CHIRAL FIELDS AS N→∞

An example of a sequence of the sl(N;C) chiral fields, for N≥2, tending to the complex heavenly metric (nonlinear graviton) of the type [4]× [-] when N→∞ is given.