# New Vacuum Solutions for Quadratic Metric-Aﬃne Gravity - a Metric Aﬃne Model for the Massless Neutrino?

Mathematica Balkanica New Series (2010)

- Volume: 24, Issue: 3-4, page 329-340
- ISSN: 0205-3217

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topPasic, Vedad. "New Vacuum Solutions for Quadratic Metric-Aﬃne Gravity - a Metric Aﬃne Model for the Massless Neutrino?." Mathematica Balkanica New Series 24.3-4 (2010): 329-340. <http://eudml.org/doc/11354>.

@article{Pasic2010,

abstract = {AMS Subj. Classiﬁcation: 83C15, 83C35In this paper we present an overview of our research that was presented at theMASSEE
International Congress on Mathematics MICOM 2009 in Ohrid, Macedonia. We deal with
quadratic metric–aﬃne gravity, which is an alternative theory of gravity. We present new
vacuum solutions for this theory and an attempt to give their physical interpretation on the
basis of comparison with existing classical models. These new explicit vacuum solutions of
quadratic metric–aﬃne gravity are constructed using generalised pp-waves. A classical pp-
wave is a 4-dimensional Lorentzian spacetime which admits a non–vanishing parallel spinor
ﬁeld. We generalise this deﬁnition to metric compatible spacetimes with torsion, describe basic
properties of such spacetimes and eventually use them to construct new solutions to the ﬁeld
equations of quadratic metric–aﬃne gravity. The physical interpretation of these solutions we
propose is that these new solutions represent a conformally invariant metric–aﬃne model for
the massless neutrino. We give a comparison with a classical model describing the interaction
of gravitational and massless neutrino ﬁelds, namely Einstein-Weyl theory. Future research
topics are brieﬂy discussed.},

author = {Pasic, Vedad},

journal = {Mathematica Balkanica New Series},

keywords = {Quadratic Metric-Aﬃne Gravity; pp-Waves; Torsion; Exact Solution; Neutrino; quadratic metric-affine gravity; pp-waves; torsion; exact solution; neutrino},

language = {eng},

number = {3-4},

pages = {329-340},

publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},

title = {New Vacuum Solutions for Quadratic Metric-Aﬃne Gravity - a Metric Aﬃne Model for the Massless Neutrino?},

url = {http://eudml.org/doc/11354},

volume = {24},

year = {2010},

}

TY - JOUR

AU - Pasic, Vedad

TI - New Vacuum Solutions for Quadratic Metric-Aﬃne Gravity - a Metric Aﬃne Model for the Massless Neutrino?

JO - Mathematica Balkanica New Series

PY - 2010

PB - Bulgarian Academy of Sciences - National Committee for Mathematics

VL - 24

IS - 3-4

SP - 329

EP - 340

AB - AMS Subj. Classiﬁcation: 83C15, 83C35In this paper we present an overview of our research that was presented at theMASSEE
International Congress on Mathematics MICOM 2009 in Ohrid, Macedonia. We deal with
quadratic metric–aﬃne gravity, which is an alternative theory of gravity. We present new
vacuum solutions for this theory and an attempt to give their physical interpretation on the
basis of comparison with existing classical models. These new explicit vacuum solutions of
quadratic metric–aﬃne gravity are constructed using generalised pp-waves. A classical pp-
wave is a 4-dimensional Lorentzian spacetime which admits a non–vanishing parallel spinor
ﬁeld. We generalise this deﬁnition to metric compatible spacetimes with torsion, describe basic
properties of such spacetimes and eventually use them to construct new solutions to the ﬁeld
equations of quadratic metric–aﬃne gravity. The physical interpretation of these solutions we
propose is that these new solutions represent a conformally invariant metric–aﬃne model for
the massless neutrino. We give a comparison with a classical model describing the interaction
of gravitational and massless neutrino ﬁelds, namely Einstein-Weyl theory. Future research
topics are brieﬂy discussed.

LA - eng

KW - Quadratic Metric-Aﬃne Gravity; pp-Waves; Torsion; Exact Solution; Neutrino; quadratic metric-affine gravity; pp-waves; torsion; exact solution; neutrino

UR - http://eudml.org/doc/11354

ER -

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