Primary Research Area:  Black holes, Asymptotic Symmetries in Gauge and Gravity Theories and aspects of Quantum field theory.  

Summary

In recent years, it has become apparent that three ostensibly disparate topics share a common underlying subject, despite originating from distinct starting points and being articulated in diverse notations. The realm of asymptotic symmetries explores the nontrivial symmetries or conserved charges inherent in any system featuring an asymptotic region or boundary of spacetime. I worked on near-horizon asymptotic symmetries of BTZ black holes and CFT correspondence in my project. I have studied a problem related to (2+1) dimensional gravity viz. AdS_3 solution in the presence of extremal  BTZ black holes.  Asymptotic symmetry analysis of this kind of spacetime enables us to identify the symmetry group and the surface charges corresponding to the asymptotic symmetry generators. The algebra of these charges can be identified with the algebra of a known conformal group of a boundary CFT. A powerful technique to study these symmetries is the Covariant Phase Space method which enables us to calculate these conserved surface charges. Using Mathematica I have calculated the centrally extended charge algebra for some asymptotic spaces with some nontrivial boundary restrictions. I further studied the near horizon BTZ black holes and the corresponding non-chiral extensions of the Conformal algebras. I applied these methods to some higher curvature theories of gravity, like new massive gravity (NMG) and topologically massive gravity (TMG), for some different boundary conditions, and I also studied its thermodynamic aspects from the CFT side. In the future, I want to study its application to Holographic RG flow and flat space Holography

Summary

This project was intended to search for the possible signature of naked singularities by studying the Kerr bound from observational pieces of evidence. This involved a detailed theoretical study of the horizon spacetime of a naked singularity, its stability analysis, relativistic jets, and accretion physics. In the end tried to theoretically model the jet launching mechanism for naked singularity spacetime. 

Summary

In this term paper, I have reproduced a paper dealing with near-field refractive index measurements and did some work and simulation on the photonic analogue of evanescently coupled potential wells to explore hopping probability, Floquet theory, and Band structures using photonic analogue, which includes data manipulation of femtosecond laser written optical waveguide, taken from Penn State research laboratory.