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arXiv · 1001.3436

Schr\"odinger-like Dilaton Gravity

Yu Nakayama
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Abstract

We investigate possibilities for a Schr\"odinger-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.

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Yu Nakayama. 2010-01-20. Schr\"odinger-like Dilaton Gravity. https://doi.org/10.3842/sigma.2011.014

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