A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities

Dec 19, 2015
46 pages
Published in:
  • JHEP 04 (2016) 145
  • Published: Apr 22, 2016
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Abstract: (Springer)
We define a ‘non-relativistic conformal method’, based on a Schrödinger algebra with critical exponent z = 2, as the non-relativistic version of the relativistic conformal method. An important ingredient of this method is the occurrence of a complex compensating scalar field that transforms under both scale and central charge transformations. We apply this non-relativistic method to derive the curved space Newton-Cartan gravity equations of motion with twistless torsion. Moreover, we reproduce z = 2 Hořava-Lifshitz gravity by classifying all possible Schrödinger invariant scalar field theories of a complex scalar up to second order in time derivatives.
Note:
  • 35 pages + appendices
  • Classical Theories of Gravity
  • Gauge Symmetry
  • field equations: gravitation
  • nonrelativistic
  • conformal
  • critical phenomena
  • central charge
  • torsion
  • Horava-Lifshitz