AR-2019-2020

both the gauge-invariant and non-invariant version- Theoretical spectra have been determined both in the Lagrangian and Hamiltonian formulation and a necessary correlation between these two is made. BRST quantization using BFV formalism has been executed, which shows spontaneous appearance of Wess-Zumino term during the process of quantiza- tion. The gauge invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition. This work has been done in col- laboratio with Sanjib Ghosal. Role of Faddeevian anomaly in the s-wave scatter- ing of chiral Fermion off dilaton black holes towards preservation of information It was found that s-wave scattering of chiral Fermion off dilaton black-hole when studied with a model generated from the chiral Schwinger model with standard Jackiw-Rajaraman type of anomaly provided information non-preserving result. How- ever, this scattering problem when studied with a model generated from chiral Schwinger model with generalized Faddeevian type of anomaly rendered information preserving result and it had well agree- ment with Hawking’s revised proposal related to information loss. A minute and equitable investi- gation in detail has been carried out here to show how Faddeevian type of anomaly scores over the Jackiw-Rajaraman type of anomaly in connection with the s-wave scattering of chiral fermion of dila- ton black-hole related to preservation of informa- tion. Farook Rahaman Gravitational collapse of an interacting vacuum en- ergy density with an anisotropic fluid We investigate the effects of anisotropic pressure on the gravitational collapse of spherically sym- metric, gravitational bound objects. The concept of a pressure anisotropy in stellar models is pro- duced by a large set of physical phenomena in high density regimes. We consider a gravitational col- lapse process of the anisotropic fluid interacting with a growing vacuum energy density. We con- sider the full general-relativistic treatment of this problem, and obtain exact solutions for various forms of the equation of state ( k, l ) : p t = kρ and p r = lρ, ( l +2 k ) < − 1 connecting the tangential and radial pressures respectively. This work has been done in collaboration with Harsat Hussain Shah, Amna Ali, and Sabiruddin Molla. Einstein’s cluster mimicking compact star in the teleparallel equivalent of general relativity The Teleparallel Gravity (TEGR) is an alternative formulation of gravity which uses tetrads as the dynamical variables. First, we develop the Ein- stein clusters in TEGR field equations using effec- tive energy-momentum tensor for diagonal as well as off-diagonal tetrad. We then study the clusters in modified f ( T ) gravity for anisotropic fluid dis- tribution. We further study the solution without net electric charge and then for charged solution. For charge parameter k → 0, the charged solution reduces to neutral one. Our calculations show that when charge increases, the stiffness of the EoS also increases. This is due to increase in adiabatic in- dex and sound speed approaching speed of light. When the charge increases beyond a certain limit (0 ≤ k ≤ 1 . 3 × 10 − 5 and 0 ≤ k ≤ 1 × 10 − 6 ), the compactness parameter crosses the Buchdahl limit, i.e., 2 M/R > 8 / 9 , and the solution starts violat- ing the causality condition. We test the Tolman- Oppenheimer-Volkoff (TOV) limit for such com- pact objects. We analyze the static stability cri- terion of the Einstein clusters for both charged and uncharged case, and the stability of such compact objects is enhanced by the presence of some net electric charge. In addition, we present and dis- cuss the energy conditions, causality condition and the adiabatic index close to the stability limit. Af- ter analyzing these problems, we conclude that the Einstein clusters do exists only if f ( T ) is a linear function of the torsion scalar T , that is, in the case of Teleparallel equivalent of General Relativity. Fi- nally, we compare our solution for pure general rel- ativity. As a result, we concluded that the Einstein cluster solution do exist in pure GR, however, phys- ically unfit to mimic compact stars. We have also extend our findings by assuming the diagonal or off- diagonal tetrad and specific case of f ( T ). In such models, Einstein’s cluster solutions do exist, how- ever, can’t mimic the properties of a compact star. This work has been done in collaboration with Ksh. Newton Singh, and Ayan Banerjee.