In this paper we will discuss Brans conjecture that exotic smoothness serves as an additional gravitational source naturally arising from the handlebody construction of the exotic $\mathbb{ R}^{ 4}$. We will consider the two possible classes, the large and the small exotic $\mathbb{ R}^{ 4}$. Then we calculate the Einstein-Hilbert action for both exotic $\mathbb{ R}^{ 4}$ to show the apearance of spinor fields. Then we discuss the physical properties of these spinor fields to relate them to fermions. Finally we identify the corresponding 3-manifolds as knot complements of hyperbolic knots, i.e. the knot complements are hyperbolic 3-manifolds with finite volume. With the help of this result we confirm the Brans conjecture for both kinds of exotic $\mathbb{ R}^{ 4}$.
Categories: gr-qc hep-th math-ph math.MP