AR-2019-2020

thick brane and the scale of the extra dimension is time-dependent. We use a simple ansatz to solve the Dirac equation in the bulk that helps us to com- pare our results with the known four dimensional case. Renormalisation of the components of the en- ergy momentum tensor is achieved using adiabatic regularization method. We compute the leading order finite contribution to the stress-energy ten- sor which is of adiabatic order six. The resulting energy and pressure densities explicitly show the effects of the so-called warping factor and the dy- namic extra dimension on the created matter. We show how the energy density produced is localised to form 3-branes along the extra dimension. Sushant G. Ghosh Shadow cast and deflection of light by charged ro- tating regular black holes We discuss the horizon properties, shadow cast, and the weak gravitational lensing of charged ro- tating regular black holes, in addition to mass ( M ) and rotation parameter ( a ) have an electric charge ( Q ) and magnetic charge ( g ). The considered are the generalization of the Kerr ( Q = g = 0) and Kerr-Newman ( g = 0) black holes. Interestingly, for a given parameter set, the apparent size of the shadow monotonically decreases and the shadow gets more distorted with increasing charge parame- ter Q . We put constraints on the black hole param- eters with the aid of recent M87* shadow observa- tion. The conserved quantities associated with the rotating regular black holes are calculated, and also a brief description of the weak gravitational lensing using the Gauss-Bonnet theorem is presented. In- terestingly, the deflection angle decreases with the charge of the black hole. Our results vis-`a-vis go over to the Kerr and Kerr-Newman black holes in the appropriate limits. This work has been done in collaboration with Rahul Kumar, and Anzhong Wang. Black hole parameter estimation from its shadow The Event Horizon Telescope (EHT), a global sub- millimeter wavelength very long baseline interfer- ometry array, unveiled event-horizon-scale images of the supermassive black hole M87* as an asym- metric bright emission ring with a diameter of 42 ± 3 μ as, and it is consistent with the shadow of a Kerr black hole of general relativity. A Kerr black hole is also a solution of some alternative the- ories of gravity, while several modified theories of gravity admit non-Kerr black holes. While ear- lier estimates for the M87* black hole mass, de- pending on the method used, fall in the range ≈ 3 × 10 9 M − 7 × 10 9 M , the EHT data indicated a mass for the M87* black hole of (6 . 5 ± 0 . 7) × 10 9 M . This offers another promising tool to estimate black hole parameters and to probe theories of gravity in its most extreme region near the event hori- zon. The important question arises: Is it possi- ble by a simple technique to estimate black hole parameters from its shadow, for arbitrary mod- els? In this work, we present observables, ex- pressed in terms of ordinary integrals, character- izing a haphazard shadow shape to estimate the parameters associated with black holes, and then il- lustrate its relevance to four different models: Kerr, Kerr − Newman, and two rotating regular models. Our method is robust, accurate, and consistent with the results obtained from existing formalism, and it is applicable to more general shadow shapes that may not be circular due to noisy data. This work has been done in collaboration with Rahul Kumar Rupjyoti Gogoi Formation of disc galaxies around Z ∼ 2 We present combined evolution of morphological and stellar properties of galaxies on the two sides of z = 2 (2.0 < z < 4.0 and 1.5 < z < 2.0) in CDFS, with ground-based spectroscopic redshifts. We per- form bulge-disc decomposition on their images in J and H filters, from the 3DHST Legacy Survey ob- tained using HST/WFC3. Combining morphologi- cal information with stellar properties, we provide a detailed account of the formation/growth of discs and spheroids around z ∼ 2. The fraction of two- component (bulge+disc) systems increases from 46 per cent for z > 2 to 70 per cent for z < 2, compen- sating for the fall in population of pure discs and pure spheroids. All quiescent outliers of our full sample on the main sequence are two-component systems, belonging to the lower redshift range (z < 2). The doubling of stellar mass of two-component systems and decrease in their SFR by the same fac- tor, suggests that mechanisms involved in morpho- logical transformations are also responsible for the quenching of their star formation activity. Interest- ingly, while there is substantial increase in the size