The geometry and phase structure of non-relativistic branes

We use the solution-generating technique, the TsT transformation, to obtain new solutions in type II string theory as well as in M-theory. We explicitly work out examples starting with rotating D3 and M2 branes as well as the D1-D5-p system. Among a variety of solutions, we find many of them having asymptotic Schrodinger symmetry. We also devise a newmethod of deriving the free energy of black brane systems, which is more efficient than the Euclidean action procedure. We test our method on known examples before applying it to new asymptotically Schrodinger backgrounds. We study the phase structure of these backgrounds by analyzing the free energy thus derived.