This talk is devoted to Berry phases that appear in the context of asymptotic symmetries in general relativity. These phases arise when a coherent state is acted upon by symmetry transformations that trace a closed path in the symmetry group, and they can be evaluated exactly even when the group is infinite-dimensional. We apply these ideas to the Virasoro and BMS groups; seeing their representations as particles dressed with boundary gravitons, the associated Berry phases generalize Thomas precession and provide, in principle, observable signatures of asymptotic symmetries.
The September 2015 detection of gravitational waves by Advanced LIGO marks the beginning of a new era in astrophysics where information from distant regions of our Universe is ``read” directly from fluctuations in the spacetime itself. General Relativity (GR) predicts that gravitational radiation changes the spacetime permanently which would show in a permanent displacement of the test masses in a detector. This phenomenon is called the memory effect of gravitational waves. In linearized theory, such an effect was first derived by Ya.B. Zel’dovich and A.G. Polnarev in 1974, and in the fully nonlinear theory by D. Christodoulou in 1991. In recent years, D. Garfinkle and myself showed that these are indeed two different effects, the former being sourced by the change of a particular component of the curvature tensor the latter by fields that reach null infinity. The latter is larger, and there have been suggestions on how to detect it by current and future gravitational wave detectors. For the first time outside of GR, D. Garfinkle and myself found an electromagnetic analog of these two types of memory a few years ago.
Recently, in joint work with D. Garfinkle and N. Yunes we showed that for sources at cosmological distances, gravitational waves and their memory effect are altered by the redshift and by a term involving gravitational lensing. In this talk, I will explain the memory effect of gravitational waves and also highlight the latest results.
University of Cambridge, Radcliffe Institute
"Black Hole Entropy from Soft Hair"