In this thesis, we discuss applications of numerical relativity in a variety of complex settings. After introducing aspects of black hole physics, extra dimensions, holography, and Einstein-Aether theory we discuss how one can frame the problem of solving the static Einstein equations as an elliptic boundary value problem by inclusion of a DeTurck gauge fixing term. Having setup this background, we turn to our simplest application of numerical relativity, namely fractionalisation in holographic condensed matter....