Research Projects

This project aims to explore the enhanced symmetry on extremal, near-extremal, and non-extremal black holes in four spacetime dimensions. The microscopic degeneracies of extremal black holes are expressed in terms of modular forms and mock modular forms, which are well-used in the study of black hole dynamics. The study will be important to understand the deep mathematical roots of black hole physics. Near extremal black holes with small temperatures have some remaining symmetries at the near horizon and can be formulated into a complete four-dimensional Euclidean action computation. An effective two-dimensional description for these black hole dynamics has been proposed, and an alternate two-dimensional effective description for supersymmetric black holes is also being explored. The study will also investigate the statistical origin of finite temperature non-extremal black holes, such as Schwarzschild, which carry thermodynamic entropy. The researchers plan to compute the BMS4 hairs of supersymmetric extremal and non-extremal black holes appearing in four-dimensional supergravity theories, examining their relation to black hole entropy. Asymptotic symmetries imply Soft theorems for gravity and gauge theories in asymptotically flat spacetime but have not been studied in detail in asymptotically non-flat spacetime, such as AdS spacetime. They aim to analyze the possibility of Soft Theorems in asymptotically AdS spacetime, first recasting the field theory Soft theorem in the language of appropriate dual variables and then providing a first principle proof for AdS Soft theorems. This will help in understanding AdS/CFT conjecture and BMS/Soft Theorem equivalence.