On spectral geometry approach to Horava-Lifshitz gravity: Spectral dimension

Abstract

We initiate the study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather corresponding generalized Laplacian), which respects both the foliation structure and anisotropic scaling, the result of Horava on a spectral dimension is reproduced for an arbitrary, non-flat space-time. The advantage and further applications of our approach are discussed.

References, a figure and minor clarifications added. To match the version to be published in CQG

References in corpus (4)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Horava-Lifshitz gravity: a status report

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