Executive Summary : | The study of the fundamental interactions of our Universe has been a growing field of research since Albert Einstein's 1916 theory of General Relativity. This theory, which is framed in a general coordinate invariant way, led to the existence of Black holes (BH). The mathematical structure of stationary BH is encoded by their event horizon (EH), a null hypersurface in a black hole that serves as a causal boundary for observers outside the horizon. The EH behaves like a thermodynamical entity satisfying mathematical equations that resemble ordinary laws of thermodynamics. The area of the EH is proportional to its entropy, which has generated many activities to decipher the underlying physics behind this fact. A stationary black hole is just a mathematical construct, and matter fields or radiation around it can make it dynamic. The entropy of a black hole is shown to be the Noether charge of the Killing symmetry of the EH. However, these laws need to be carefully verified for dynamic situations, such as quasi-local horizons mimicking practical situations like black hole mergers. This proposal aims to study the aspects of horizons of dynamical black holes using analytic and semi-analytic approaches. The Bondi-Metzner-Sachs group (BMS) group contains infinite-dimensional symmetries, Supertranslations and Superrotations, which contribute to the black hole's entropy. Researchers will address the subtle issues in defining superrotation charges and explore the relationship between these symmetries and the gravitational Memory effect. |