Lifshitz/Schrödinger D-p-branes and dynamical exponents

We extend our earlier study of special double limits of `boosted' $AdS_5$ black hole solutions to include all black D$p$-branes of type II strings. We find that Lifshitz solutions can be obtained in generality, with varied dynamical exponents, by employing these limits. We then study such double limits for `boosted' D$p$-brane bubble solutions and find that the resulting non-relativistic solutions instead describe Schrödinger like spacetimes, having varied dynamical exponents. We get a simple map between these Lifshitz & Schrödinger solutions and a relationship between two types of dynamical exponents. We also discuss about the singularities of the Lifshitz solutions and an intriguing thermodynamic duality.

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