Geometric Algebra, Dirac Wavefunctions and Black Holes

In this contribution we describe some applications of geometric algebra to the field of black hole physics. Our main focus is on the properties of Dirac wavefunctions around black holes. We show the existence of normalised bound state solutions, with an associated decay rate controlled by an imaginary contribution to the energy eigenvalue. This is attributable to the lack of Hermiticity caused by a black hole singularity. We also give a treatment of the Feynman scattering problem for fermions interacting with black holes that we believe is new, and produces an analogue of the Mott scattering formula for the gravitational case. Throughout, the consistent application of geometric algebra simplifies the mathematical treatment and aids understanding by focusing attention on observable quantities. We finish with a brief review of recent work on the effects of torsion in quadratic theories of gravity. This work demonstrates that a free torsion field can play a significant role in cosmology.

Anthony Lasenby and Chris Doran, Geometric Algebra, Dirac Wavefunctions and Black Holes, In P.G. Bergmann and V. de Sabbata eds, Advances in the Interplay Between Quantum and Gravity Physics, 251-283, Kluwer (2002)