Einstein GR is dead, viva Einstein-Cartan Gravity?

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Based on the wiki article:


Cartan gravity is not just “possible extension” of GR, but it is absolutely necessary and unavoidable (search for “proof” in the article). As wiki is not a 100% trusted source, I wanted to ask: How widely is that accepted?
This article is extremely questionable. I've never even heard of the topic, but many of the points in the article are incorrect, not to mention the entire tone/style is very inappropriate. You should take a look at its 'discussion' page.


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I would like to make an important point: the General Theory of Relativity is entirely a classical theory. An extension of it to a space-time with torsion is not bringing any new classical physics. It may be appropriate to encorporate quantum elements (like spin), but that's already a glimpse from a long sought different theory: namely the quantum theory of gravitation. The suggested theory in the wiki page is more of a semiclassical story. However, that can't be really accepted, unless we invalidate anything we know about quantum mechanics, in the sense of lowering our knowledge of quantum mechanics as to accept semiclassical theories.

So Einstein's GR is not dead and not yet coherently extended by a mathematical rigorous quantum theory of gravitation.

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as a result, dont trust wiki.


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as a result, dont trust wiki.
I trust Wikipedia more than I trust peer reviewed journals, because the peer reviewed stuff is never corrected. The lesson here would be to not trust Wikipedia articles that start with "This article needs attention from an expert on the subject" and have people fighting on the discussion page.
In any case, Kerrs solution for the rotating BH is made in GR framework.
Is it different in GR+cartans extension?


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I have studied many articles regarding (candidate) theories for quantum gravity, especially loop quantum gravity. In the context of these theories it seems natural to extend the concept of Riemannian spacetime to Riemann-Cartan spacetime and to study Einstein-Cartan instead of Einstein-Hilbert gravity.

Phenomenologically ECT is no required classically b/c torsion is non-propagating and therefore exactly zero in vacuum (restricted to the non-vacuum as defined by non-vanishing of the energy-momentum tensor). Torsion effects are not measurable as spin-density is suppressed classically due to the smallness of the graviational constant.

The reasons are more mathematical and conceptual; there are (as of today) no physical (phenomenological) indications to do this. Nevertheles the reasons seem to be rather convincing.

EC allowes one to incorporate a local gauge principle in the theory and to use well-known methods from ordinary gauge theories. Essentially ECT is a special gauge theoriy plus diffeomorphism invariance.
EC allowes for a natural implementation of spin, spinor fields and their coupling to space time.
EC "solves" conceptual problems of the LQG program (these difficulties arise in the context of quantization; they intrinsically to that approach, so one may argue that instead of using themas indication for ECT one could also use them as indications against LQG). EC allowes one to interpret a quantization ambiguity (the Immirzi parameter) in a similar way as the theta angle in QCD. That seems to be rather natural.

There are forst indications that ECT differs not only when LQG methods are applied, but also when the asymptotoc safety (non-perturbative renormalization) approach is used.

This aproaches seems to indicate that GR can be renormalized non-perturbatively b/c it seems to have a non-Gaussian fixed point of the renormalization group flow. That means that usual perturbative definitions still break down b/c zero Newtonian constant is not a good starting point. But non-vanishing G and non-vanishing cosmological constant may allow for a renormalization program.

If one uses this AS approach to study ECT instead of Einstein-Hilbert GR there are indications that there are fixed points for the Immirzi paraneter value zero and infinity. If this is true then these to fixed points allow for a "continuum limit". It seems to be the case (but the results are very premature) that the continuum limit of ECT differs from standard GR. That would mean that in the quantum gravity regime there may be indeed phenomenological reasons which could rule out either q-GR or q-ECT.


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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.

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.

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.

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.

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.

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