We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section for a range of gravitational couplings Mm/m_P^2 and incident particle … Continued
We compute the spectrum of normalizable fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a hydrogen-like spectrum. The imaginary parts give decay times … Continued
Conformal embedding of closed-universe models in a de Sitter background suggests a quantisation condition on the available conformal time. This condition implies that the universe is closed at no greater than the 10% level. When a massive scalar field is … Continued
Blending schemes based on circles provide smooth `fair’ interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity can be achieved by … Continued
Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in … Continued
In the surface acoustic wave quantum computer, the spin state of an electron trapped in a moving quantum dot comprises the physical qubit of the scheme. Via detailed analytic and numerical modeling of the qubit dynamics, we discuss the effect … Continued
Lecture delivered in the Cavendish Laboratory, Cambridge, 2004. PDF
A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting … Continued
We review the applications of geometric algebra geometric algebra in electromagnetism, gravitation and multiparticle quantum systems. We discuss a gauge theory formulation of gravity and its implementation in geometric algebra, and apply this to the fermion bound state problem in … Continued
The differential cross section for scattering of a Dirac particle in a black hole background is found. The result is the gravitational analog of the Mott formula for scattering in a Coulomb background. The equivalence principle is neatly embodied in … Continued