1205.2586 (Ovidiu Cristinel Stoica)

Quantum Gravity from Metric Dimensional Reduction at Singularities    [PDF]

Ovidiu Cristinel Stoica

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the cause of this dimensional reduction would still be desirable. A possible explanation of the dimensional reduction is suggested by recent results in understanding the geometry of singularities in General Relativity. These new methods don't require modification of General Relativity, being just extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. Therefore, it seems that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity.

View original: http://arxiv.org/abs/1205.2586