http://arxiv.org/abs/gr-qc/0606062
Einstein-Cartan Theory
Andrzej Trautman
(Submitted on 14 Jun 2006)
Abstract: The Einstein--Cartan Theory (ECT) of gravity is a modification of General Relativity Theory (GRT), allowing space-time to have torsion, in addition to curvature, and relating torsion to the density of intrinsic angular momentum. This modification was put forward in 1922 by Elie Cartan, before the discovery of spin. Cartan was influenced by the work of the Cosserat brothers (1909), who considered besides an (asymmetric) force stress tensor also a moments stress tensor in a suitably generalized continuous medium.
http://arxiv.org/abs/gr-qc/9712096
Alternative Gravitational Theories in Four Dimensions
Friedrich W. Hehl (University of Cologne)
(Submitted on 26 Dec 1997)
Abstract: We argue that from the point of view of gauge theory and of an appropriate interpretation of the interferometer experiments with matter waves in a gravitational field, the Einstein-Cartan theory is the best theory of gravity available. Alternative viable theories are general relativity and a certain teleparallelism model. Objections of Ohanian and Ruffini against the Einstein-Cartan theory are discussed. Subsequently we list the papers which were read at the `Alternative 4D Session' and try to order them, at least partially, in the light of the structures discussed.
http://arxiv.org/abs/arXiv:gr-qc/9602013
On the Gauge Aspects of Gravity
F. Gronwald, F.W. Hehl
(Submitted on 8 Feb 1996)
Abstract: We give a short outline, in Sec.\ 2, of the historical development of the gauge idea as applied to internal ($U(1),\, SU(2),\dots$) and external ($R^4,\,SO(1,3),\dots$) symmetries and stress the fundamental importance of the corresponding conserved currents. In Sec.\ 3, experimental results with neutron interferometers in the gravitational field of the earth, as inter- preted by means of the equivalence principle, can be predicted by means of the Dirac equation in an accelerated and rotating reference frame. Using the Dirac equation in such a non-inertial frame, we describe how in a gauge- theoretical approach (see Table 1) the Einstein-Cartan theory, residing in a Riemann-Cartan spacetime encompassing torsion and curvature, arises as the simplest gravitational theory. This is set in contrast to the Einsteinian approach yielding general relativity in a Riemannian spacetime. In Secs.\ 4 and 5 we consider the conserved energy-momentum current of matter and gauge the associated translation subgroup. The Einsteinian teleparallelism theory which emerges is shown to be equivalent, for spinless matter and for electromagnetism, to general relativity. Having successfully gauged the translations, it is straightforward to gauge the four-dimensional affine group $R^4 \semidirect GL(4,R)$ or its Poincar\'e subgroup $R^4\semidirect SO(1,3)$. We briefly report on these results in Sec.\ 6 (metric-affine geometry) and in Sec.\ 7 (metric-affine field equations (\ref{zeroth}, \ref{first}, \ref{second})). Finally, in Sec.\ 8, we collect some models, currently under discussion, which bring life into the metric-affine gauge framework developed.
http://arxiv.org/abs/0907.0934
On the Poincare Gauge Theory of Gravitation
S. A. Ali, C. Cafaro, S. Capozziello, Ch. Corda
(Submitted on 6 Jul 2009 (v1), last revised 16 Dec 2009 (this version, v2))
Abstract: We present a compact, self-contained review of the conventional gauge theoretical approach to gravitation based on the local Poincare group of symmetry transformations. The covariant field equations, Bianchi identities and conservation laws for angular momentum and energy-momentum are obtained.
http://arxiv.org/abs/1010.5822
Gauge Gravity: a forward-looking introduction
Andrew Randono
(Submitted on 27 Oct 2010)
Abstract: This article is a review of modern approaches to gravity that treat the gravitational interaction as a type of gauge theory. The purpose of the article is twofold. First, it is written in a colloquial style and is intended to be a pedagogical introduction to the gauge approach to gravity. I begin with a review of the Einstein-Cartan formulation of gravity, move on to the Macdowell-Mansouri approach, then show how gravity can be viewed as the symmetry broken phase of an (A)dS-gauge theory. This covers roughly the first half of the article. Armed with these tools, the remainder of the article is geared toward new insights and new lines of research that can be gained by viewing gravity from this perspective. Drawing from familiar concepts from the symmetry broken gauge theories of the standard model, we show how the topological structure of the gauge group allows for an infinite class of new solutions to the Einstein-Cartan field equations that can be thought of as degenerate ground states of the theory. We argue that quantum mechanical tunneling allows for transitions between the degenerate vacua. Generalizing the tunneling process from a topological phase of the gauge theory to an arbitrary geometry leads to a modern reformulation of the Hartle-Hawking "no boundary" proposal.
