Geodesic
Schrödinger-like Dilaton Gravity
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate possibilities for a Schrödinger-like gravity with the dynamical critical exponent $z=2$, where the action only contains the first-order time derivative. The Horava gravity always admits such a relevant deformation because the full ($d+1$) dimensional diffeomorphism of the Einstein gravity is replaced by the foliation preserving diffeomorphism. The dynamics is locally trivial or topological in the pure gravity case, but we can construct a dynamical field theory with a $z=2$ dispersion relation by introducing a dilaton degree of freedom. Our model provides a classical starting point for the possible quantum dilaton gravity which may be applied to a membrane quantization.
Keywords: non-relativistic gravity; membrane quantization. 
@article{SIGMA_2011_7_a13,
     author = {Yu Nakayama},
     title = {Schr\"odinger-like {Dilaton} {Gravity}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a13/}
}
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Yu Nakayama. Schrödinger-like Dilaton Gravity. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a13/

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