Black holes are perhaps one of the most fascinating predictions of Einstein's theory. These objects are completely gravitationally collapsed objects with such immense gravitational fields that not even light can escape its pull. Within General Relativity, the two most famous black hole solutions were discovered by Schwarzschild and Kerr, which represent non-spinning and spinning black holes in isolation, respectively. But black holes, like any other object in the Universe, do not exist in isolation. These objects are in constant interactions with matter and with gravitational fields from other stars in their surroundings. Such interactions perturb the Schwarzschild and Kerr solutions, inducing dynamics that tidally heat and torque the perturbed black hole.

The XGI uses black hole perturbation theory to study such dynamical environments and determine how the mass, angular momentum, surface area and spacetime metric of Schwarzschild and Kerr black holes are affected by perturbing forces. These perturbations are important because they affect the gravitational waves emitted when two black holes inspiral. Any one black hole in a binary is constantly being perturbed by its companion, tidally torquing and heating it, which then translates to modifications in their orbital motion and the gravitational waves emitted.

Once a perturbed black hole spacetime metric is obtained, one can use it to find the dynamical spacetime metric of a binary system. This is achieved by asymptotically matching the perturbed solution, valid close to either binary component, to a post-Newtonian metric valid sufficiently far away from either companion. These two metrics have overlapping regions of validity, inside which they can be related through certain multiple scale analysis techniques. Once a global dynamical metric is obtained, this can be used as initial data for numerical simulations, or as a dynamical background in which to study certain astrophysical processes, such as accretion in thin disks.