Quadratic non-Riemannian Gravity

In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. We then introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. This definition was generalised in our previous work to metric compatible spacetimes with torsion and used to construct new explicit vacuum solutions of quadratic metric-affine gravity, namely generalised pp-waves of parallel Ricci curvature. The physical interpretation of these solutions we propose in this article is that they represent a conformally invariant metric-affine model for a massless elementary particle. We give a comparison with the classical model describing the interaction of gravitational and massless neutrino fields, namely Einstein-Weyl theory and construct pp-wave type solutions of this theory. We point out that generalised pp-waves of parallel Ricci curvature are very similar to pp-wave type solutions of the Einstein-Weyl model and therefore propose that our generalised pp-waves of parallel Ricci curvature represent a metric-affine model for the massless neutrino.

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“…See e.g. [1,5,8,10,21,23,38,48,49,51,53,57,58,70,71] for more information on pp-waves and pp-wave type solutions of metricaffine gravity.…”

Section: Classical Pp-wavesmentioning

confidence: 99%

“…The observation that one can construct vacuum solutions of quadratic metricaffine gravity in terms of pp-waves is a recent development. The fact that classical pp-spaces of parallel Ricci curvature are solutions was first pointed out in [69,70,71].…”

Section: Physical Interpretation Of Generalised Pp-wavesmentioning

confidence: 99%

PP-waves with torsion: a metric-affine model for the massless neutrino

Pasic

Barakovic

2014

Gen Relativ Gravit

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“…• The second term in the RHS of (16) is pure gauge in the sense that it does not affect curvature (19). It does, however, affect torsion (17).…”

Section: Pp-waves With Torsionmentioning

confidence: 99%

“…The fact that classical pp-spaces of parallel Ricci curvature are solutions was first pointed out in [18,19,2].…”

Section: Comparison With Existing Literaturementioning

confidence: 99%

pp-waves with torsion and metric-affine gravity

Pasic

Vassiliev

2005

Class. Quantum Grav.

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Abstract. A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity.

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“…The torsion T is purely axial and the connection of a generalised pp-wave with purely axial torsion is metric compatible. We have shown that generalised pp-waves with purely axial torsion of parallel {Ric} are solutions of (1), (2) in the Yang-Mills case. The remarkable property is that the curvature of a generalised pp-wave is a sum of the curvature of the underlying classical pp-space…”

Section: Introductionmentioning

confidence: 99%

Physical interpretation of pp-waves with axial torsion

Barakovic

Pasic

2017

The Fourteenth Marcel Grossmann Meeting

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We consider generalised pp-waves with purely axial torsion, which we previously showed to be new vacuum solutions of quadratic metric-affine gravity. Our analysis shows that classical pp-waves of parallel Ricci curvature should not be viewed on their own. They are a particular representation of a wider class of solutions, namely generalised pp-waves of parallel Ricci curvature. We compare our pp-waves with purely axial torsion to solutions of Einstein-Weyl theory, the classical model describing the interaction of gravitational and massless neutrino fields.

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Quadratic non-Riemannian Gravity

Cited by 4 publications

References 9 publications

PP-waves with torsion: a metric-affine model for the massless neutrino

PP-waves with torsion: a metric-affine model for the massless neutrino

pp-waves with torsion and metric-affine gravity

Physical interpretation of pp-waves with axial torsion

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