General Relativity & Quantum Cosmology

In this talk I will discuss some recent results on boundary degrees of freedom (or edge modes), and their description via an extended phase space structure containing extra boundary fields. Motivated by a slight modification of the covariant phase space formalism, I will show how the use of a boundary Lagrangian enables to include the edge modes in the phase space and to obtain their boundary dynamics. This will be illustrated on the example of Maxwell theory, where in addition the edge modes can be understood as contributing to entanglement entropy. The possible extension of this result to gravity will then be mentioned.

Recent observations of gravitational waves represent a remarkable success of our theoretical models of relativistic binaries. However, accurate models are largely restricted to binaries in which the two members have roughly equal masses; for binaries with more disparate masses, modelling is less mature. This is especially relevant for extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass object orbits a supermassive black hole in a galactic core. EMRIs are uniquely precise probes of black hole spacetimes, and they will be key targets for the space-based detector LISA. They are best modelled by gravitational self-force theory, in which the smaller object generates a small gravitational perturbation that reacts back on it to exert a "self-force", accelerating the object away from geodesic motion. For LISA science, we must work to second order in this perturbative treatment. In this talk, I discuss the foundations of self-force theory, its application to EMRIs, and the current status of first- and second-order models.