Appears in collection : 2024 - PC1 - WS - Curved spacetimes, field theory and beyond

I will review recent developments in metric reconstruction theory, i.e., the task of parameterizing GR in terms of a single complex scalar field. I will focus on the GHZ (after Green, Hollands, Zimmerman) procedure of solving the sourced linearized (or -th perturbative order-) Einstein equations in Kerr in terms of a Hertz potential. Time permitting, I will also outline other reconstruction methods such as ones based on the Lorenz gauge due to Dolan et al., or the AAB method (after Aksteiner, Anderson, Bäckdahl).