Einstein–Cartan Theory

Trautman, Andrzej

doi:10.1016/b0-12-512666-2/00014-6

Cited by 202 publications

(254 citation statements)

References 9 publications

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“…In this sense, the model under consideration is similar to the EinsteinCartan theory that also reduces to Einstein's general relativity in absence of the sources with spin, see [5,13].…”

Section: Discussionmentioning

confidence: 99%

An Assessment of Evans’ Unified Field Theory II

Hehl

Obukhov

2007

Found Phys

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Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.

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“…In this sense, the model under consideration is similar to the EinsteinCartan theory that also reduces to Einstein's general relativity in absence of the sources with spin, see [5,13].…”

Section: Discussionmentioning

confidence: 99%

An Assessment of Evans’ Unified Field Theory II

Hehl

Obukhov

2007

Found Phys

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“…If we relax the former constraint, T α = 0, we arrive at the Riemann-Cartan (RC) spacetime of the viable EinsteinCartan theory of gravity, see [9,27,52,75]. Since still Q αβ = 0, such a RC-spacetime carries a metric-compatible connection and, accordingly, a length is invariant under parallel displacement.…”

Section: Metric-affine Geometry Of Spacetimementioning

confidence: 99%

Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

2005

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We show that the Einstein-aether theory of Jacobson and Mattingly (J&M) can be understood in the framework of the metric-affine (gauge theory of) gravity (MAG).We achieve this by relating the aether vector field of J&M to certain post-Riemannian nonmetricity pieces contained in an independent linear connection of spacetime.Then, for the aether, a corresponding geometrical curvature-square Lagrangian with a massive piece can be formulated straightforwardly. We find an exact spherically symmetric solution of our model.

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“…Within the EC-theory, the energy-momentum law reads, see Sciama, Kibble, and others [36,38,51,57,66,71,72],…”

Section: Energy-momentum and Angular Momentum Lawsmentioning

confidence: 99%

“…Incidentally, in four dimensions, RC-geometry was first applied in the viable Einstein-Cartan(-Sciama-Kibble) theory of gravity, for short EC-theory [35,36,51,66,67,71,72].…”

Section: Defining Rc-geometrymentioning

confidence: 99%

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An Assessment of Evans’ Unified Field Theory I

Hehl

Obukhov

2007

Found Phys

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Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ αβ . These two potentials yield the field strengths torsion T α and curvature R αβ . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended electromagnetic potentials A α ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.

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Einstein–Cartan Theory

Cited by 202 publications

References 9 publications

An Assessment of Evans’ Unified Field Theory II

An Assessment of Evans’ Unified Field Theory II

Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity

An Assessment of Evans’ Unified Field Theory I

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