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)
Abstract: 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.