Abstract
We determine the more general geometrical flow in the space of metrics corresponding to the steepest descent for the three-dimensional gravitational Chern-Simons action, extending the results previously considered in Class. Quantum Grav. 25 (2008) 165019, and reveling another trouble with the four dimensional Hořava-Lifshitz gravity introduced in Phys. Rev. D 79, 084008 (2009), and JHEP 0903, 020 (2009), which attempts to be a candidate for an UV completion of Einstein general relativity.
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