Black Holes and Exotic Spinors

J Da Silva,C Villalobos,Roldao Da Rocha

doi:10.3390/universe2020008

Abstract

Exotic spin structures are non-trivial liftings, of the orthogonal bundle to the spin bundle, on orientable manifolds that admit spin structures according to the celebrated Geroch theorem. Exotic spin structures play a role of paramount importance in different areas of physics, from quantum field theory, in particular at Planck length scales, to gravity, and in cosmological scales. Here, we introduce an in-depth panorama in this field, providing black hole physics as the fount of spacetime exoticness. Black holes are then studied as the generators of a non-trivial topology that also can correspond to some inequivalent spin structure. Moreover, we investigate exotic spinor fields in this context and the way exotic spinor fields branch new physics. We also calculate the tunneling probability of exotic fermions across a Kerr-Sen black hole, showing that the exotic term does affect the tunneling probability, altering the black hole evaporation rate. Finally we show that it complies with the Hawking temperature universal law.

Highlights

Black holes (BHs) are most known in literature by their idiosyncratic role in the appreciation of the physical laws associated to them
In order to achieve half-integer representations of the Poincaré group, it is necessary to resort to the tangent bundle concept, which, in turn, is constructed from the union of all tangent spaces to the base manifold
Relativity can be partially incorporated in quantum field theory with the requirement of the Lorentz invariance under the Lorentz group SL(2, C) ' Spin+ (1,3), namely, the spin group associated with Minkowski spacetime, which is the double covering of SO(1, 3)

Summary

Introduction

Black holes (BHs) are most known in literature by their idiosyncratic role in the appreciation of the physical laws associated to them. The peculiarity here rests upon the fact that, spacetime being a curved base manifold, the very existence of BHs can be faced as generating non-trivial topologies. We delve into this question for the following reason: it is a very well-known fact that only vector/tensorial objects are naturally accommodated in a theory based on general coordinates transformation, as GR. In order to achieve half-integer representations of the Poincaré group, it is necessary to resort to the tangent bundle concept, which, in turn, is constructed from the union of all tangent spaces to the base manifold.

Topological Effects of a Spacetime Riddled by Black Holes

Conclusions