Lifshitz/Schr\"odinger D-p-branes and dynamical exponents

TL;DR

This paper generalizes the construction of Lifshitz and Schr"odinger spacetimes from boosted D$p$-brane solutions, revealing a relationship between their dynamical exponents and discussing singularities and thermodynamic dualities.

Contribution

It introduces a unified framework for deriving Lifshitz and Schr"odinger solutions from D$p$-branes with varied exponents, expanding previous special cases.

Findings

Lifshitz solutions with varied dynamical exponents obtained from D$p$-branes.

Schr"odinger-like spacetimes derived from boosted D$p$-brane bubbles.

A relationship established between Lifshitz and Schr"odinger exponents.

Abstract

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 Schr\"odinger like spacetimes, having varied dynamical exponents. We get a simple map between these Lifshitz & Schr\"odinger 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.