Constructing Lifshitz spaces using the Ricci flow

Abstract

In this work we make use of the Ricci flow equations to show that, by starting from a general arbitrary ansatz for the metric, we construct Lifshitz spaces in which: (a) the critical exponent takes discrete values since coincides with the spatial dimension of the spacetime and consequently, (b) by knowing the solution to the discrete case, a more general solution with continuous critical exponent was obtained. These results show that Lifshitz spaces are exact solutions to the Ricci flow equations. Moreover, we found a single fixed point along the flow for both cases which coincides with the flat spacetime.