A. N. Lasenby, C. J. L. Doran and S. F. Gull.
Gravity, gauge theories and geometric algebra
Phil. Trans. R. Soc. Lond. A356, 487-582 (1998).
Abstract: A new gauge theory of gravity is presented. The
theory is constructed in a flat background spacetime and employs
gauge fields to ensure that all relations between physical quantities
are independent of the position and orientation of the matter fields.
In this manner all properties of the background spacetime are removed
from physics, and what remains are a set of `intrinsic' relations
between physical fields. For a wide range of phenomena, including
all present experimental tests, the theory reproduces the predictions
of general relativity. Differences do emerge, however, through the
first-order nature of the equations and the global properties of
the gauge fields, and through the relationship with quantum theory.
The properties of the gravitational gauge fields are derived from
both classical and quantum viewpoints. Field equations are then
derived from an action principle, and consistency with the minimal
coupling procedure selects an action which is unique up to the possible
inclusion of a cosmological constant. This in turn singles out a
unique form of spin-torsion interaction. A new method for solving
the field equations is outlined and applied to the case of a time-dependent,
spherically-symmetric perfect fluid. A gauge is found which reduces
the physics to a set of essentially Newtonian equations. These equations
are then applied to the study of cosmology, and to the formation
and properties of black holes. Insistence on finding global solutions,
together with the first-order nature of the equations, leads to
a new understanding of the role played by time reversal. This alters
the physical picture of the properties of a horizon around a black
hole. The existence of global solutions enables one to discuss the
properties of field lines inside the horizon due to a point charge
held outside it. The Dirac equation is studied in a black hole background
and provides a quick (though ultimately unsound) derivation of the
Hawking temperature. Some applications to cosmology are also discussed,
and a study of the Dirac equation in a cosmological background reveals
that the only models consistent with homogeneity are spatially flat.
It is emphasised throughout that the description of gravity in terms
of gauge fields, rather than spacetime geometry, leads to many simple
and powerful physical insights. The language of `geometric algebra'
best expresses the physical and mathematical content of the theory
and is employed throughout. Methods for translating the equations
into other languages (tensor and spinor calculus) are given in appendices.
Original Version: pdf, postscript
Updated version avialable at: gr-qc/0405033