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There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena.
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1923
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E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée. (première partie) (Suite)
1924
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E. Inonu and E. P. Wigner, On the Contraction of groups and their represenations
1953
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V. Bargmann, On Unitary ray representations of continuous groups
1954
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H. Dombrowski and K. Horneffer, Die Differentialgeometrie des Galileischen Relativitätsprinzips
1964
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J. Luttinger, Theory of Thermal Transport Coefficients
1964
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Prentice-Hall, 1965
A. Trautman, Foundations and current problems of General Relativity · 1965
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H. P. Künzle, Galilei and Lorentz structures on space-time - comparison of the corresponding geometry and physics
1972
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M. Le Bellac and J. Lévy-Leblond, Galilean electromagnetism
1973
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W. H. Freeman and Company, 1974
C. W. Misner, K. Thorne, and J. Wheeler, Gravitation · 1974
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W. Dixon, On the uniqueness of the Newtonian theory as a geometric theory of gravitation
1975
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H. P. Künzle, Covariant Newtonian limit of Lorentz space-times
1976
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K. Kuchař, Gravitation, geometry, and nonrelativistic quantum theory
1980
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Duval, C. and Künzle, H.P., Minimal Gravitational Coupling in the Newtonian Theory and the Covariant Schrodinger Equation
1984
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H. Goenner, A variational principle for Newton-Cartan theory
1984
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The University of Chicago Press, 1984
R. M. Wald, General Relativity · 1984
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C. Duval, G. Burdet, H. P. Künzle, and M. Perrin, Bargmann structures and Newton-Cartan theory
1985
Earlier work this paper cites.
B. Julia and H. Nicolai, Null-Killing vector dimensional reduction and Galilean geometrodynamics
1995
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J. Ehlers, Examples of Newtonian limits of relativistic spacetimes
1997
Cited alongside, same era.
Cambridge University Press, 2005
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations · 2005
Cited alongside, same era.
D. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
2006
Cited alongside, same era.
C. Duval and P. A. Horvathy, Non-relativistic conformal symmetries and Newton-Cartan structures
2009
Cited alongside, same era.
Oxford University Press, 2009
Y. Choquet-Bruhat, General Relativity and the Einstein Equations · 2009
Cited alongside, same era.
American Mathematical Society, Providence, RI, second ed., 2010
L. C. Evans, Partial differential equations · 2010
2014
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2014
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M. Geracie, K. Prabhu, and M. M. Roberts, Fields and fluids on curved non-relativistic spacetimes
2015
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2015
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M. Geracie and D. T. Son, Hydrodynamics on the lowest Landau level
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Cited alongside, same era.
R. Andringa, E. Bergshoeff, S. Panda, and M. de Roo, Newtonian Gravity and the Bargmann Algebra
2011
Cited alongside, same era.
Cambridge University Press, 2011
T. Frankel, The geometry of physics: An introduction · 2011
Cited alongside, same era.
C. Hoyos and D. T. Son, Hall Viscosity and Electromagnetic Response
2012
Cited alongside, same era.
R. Andringa, E. Bergshoeff, J. Gomis, and M. de Roo, ’Stringy’ Newton-Cartan Gravity
2012
Cited alongside, same era.
University of Chicago Press, 2012
D. B. Malament, Topics in the foundations of general relativity and Newtonian gravitation theory · 2012
Cited alongside, same era.
R. Andringa, E. A. Bergshoeff, J. Rosseel, and E. Sezgin, 3D Newton–Cartan supergravity
2013
Cited alongside, same era.
2015
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M. Geracie and D. T. Son, Thermal Transport in a Noncommutative Hydrodynamics
2015
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A. Gromov and A. G. Abanov, Thermal Hall Effect and Geometry with Torsion
2015
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M. Geracie, D. T. Son, C. Wu, and S.-F. Wu, Spacetime Symmetries of the Quantum Hall Effect
2015
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2015
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2015
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J. Hartong, E. Kiritsis, and N. A. Obers, Lifshitz space–times for Schrödinger holography
2015
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2015
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J. Hartong and N. A. Obers, Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry
2015
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2015
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2015
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K. Jensen and A. Karch, Revisiting non-relativistic limits
2015
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