Dynamical construction of Horava-Lifshitz geometry

Understand

We derive the projectable version of Horava - Lifshitz gravity from the localisation of the Galilean symmetry.

• Specifically we provide a dynamical construction of the metric, from first principles, that reproduces the transformations of the physical variables - lapse, shift and spatial component of the metric.
• Also, the measure defining the action is reproduced.
• The geometrical basis of the Horava-Lifshitz gravity is thereby revealed which also elucidates its difference from the Newton-Cartan geometry - the spacetime of Newtonian gravity.