Six Lectures at the United Center for Gravitational Waves Summer School; August 2021

Since the first detection of Gravitational Waves six years ago, the field has literally exploded in multiple directions that include multi-wavelength astronomy and astrophysics, approximation methods in general relativity, numerical relativity, application of Machine Learning to waveform model building, forefront cosmological issues such as the Hubble tension, and nuclear physics issues related to the equation of state of neutron stars and nuclear processes at extreme temperature. Therefore Gravitational Wave Science has emerged as one of the most exciting research areas that now attracts young researchers in large numbers. At the same time this very explosion of the field makes it difficult for young researchers to grasp, even in broad terms, the conceptual and mathematical foundation of the theory of Gravitational Waves since the investigations that built these foundations are rarely discussed in the specific areas these researchers work in everyday. The purpose of these six lectures by Abhay Ashtekar is to fill this gap. The notion of radiation’ requires global and rather subtle constructions. Because of these subtleties, there was considerable confusion even about the physical reality of gravitational waves in full general relativity for several decades! This confusion was dispelled, thanks to a beautiful interplay between physics and geometry. Every theoretical researcher in the field should be aware of how difficulties associated with coordinate invariance are overcome and fully gauge invariant quantities representing physical observables are extracted. This awareness would provide a broad perspective that can guide their own research. Furthermore, as discussed in the last two lectures, foundational issues can also have concrete applications in addressingpractical issues’.