AR_final file_2018-19

tion involving the change in entanglement entropy known to be an analogous relation to the first law of thermodynamics. This work has been done in collaboration with Sourav Karar. Sunandan Gangopadhyay and nNir- ban Saha Footprint of spatial non commutativity in resonant detectors of gravitational wave The present day gravitational wave (GW) detec- tors strive to detect the length variation δL = hL , which owing to the smallness of the metric per- turbation ∼ h , is an extremely small length O ∼ 10 − 18 − 10 − 21 m. The recently proposed non com- mutative structure of space has a characteristic length-scale √ θ , which has an estimated upper- bound in similar length-scale range. We, therefore, propose that GW data can be used as an effective probe of non commutative structure of space and demonstrate how spatial non commutativity modi- fies the responding frequency of the resonant mass detectors of GW and also the corresponding proba- bilities of GW induced transitions that the phonon modes of the resonant mass detectors undergo. In this work, we present the complete perturbative calculation involving both time-independent and time-dependent perturbation terms in the Hamil- tonian. This work has been done in collaboration with Sukanta Bhattacharyya, and Anirban Saha. Suman Ghosh Renormalized stress tensor of a quantized massless scalar field in warped cosmological braneworld back- ground Energy momentum tensor of a conformally coupled quantum scalar field in five dimensional warped cosmological spacetimes is studied. We look at sit- uations where the four dimensional part represents a cosmological thick brane, and the scale of the ex- tra dimension is time dependent. Renormalization of the components of the energy momentum ten- sor is done using adiabatic regularization method. The resulting energy and pressure densities explic- itly show the effects of warping and the dynamic nature of the extra dimension on the created mat- ter. We discussed how the created matter accumu- late to form a thick brane near specific locations along the extra dimension. Sushant G. Ghosh Regular black holes in Einstein-Gauss-Bonnet grav- ity Einstein-Gauss-Bonnet theory, a natural general- ization of general relativity to a higher dimension, admits a static spherically symmetric black hole, which was obtained by Boulware and Deser. This black hole is similar to its general relativity coun- terpart with a curvature singularity at r = 0. We present an exact 5 D regular black hole metric, with parameter ( k > 0), that interpolates between the Boulware-Deser black hole ( k = 0) and the Wilt- shire charged black hole ( r >> k ). Owing to the appearance of the exponential correction fac- tor ( e − k/r 2 ), responsible for regularizing the metric, the thermodynamical quantities are modified, and it is demonstrated that the Hawking-Page phase transition is achievable. The heat capacity diverges at a critical radius r = r C , where incidentally the temperature is maximum. Thus, we have a reg- ular black hole with Cauchy and event horizons, and evaporation leads to a thermodynamically sta- ble double-horizon black hole remnant with vanish- ing temperature. The entropy does not satisfy the usual exact horizon area result of general relativ- ity. This work has been done in collaboration with Dharam Veer Singh, and Sunil D. Maharaj. Shadows of rotating five-dimensional charged EMCS black holes Higher dimensional theories admit astrophysical objects like supermassive black holes, which are rather different from standard ones and their grav- itational lensing features deviate from general rel- ativity. It is known that a black hole shadow is a dark region due to the falling geodesics of photons into the black hole and if detected, a black hole shadow could be used to determine, in which theory of gravity is consistent with obser- vations. Measurements of the shadow sizes around the black holes can help to evaluate various param- eters of black hole metric. We study the shapes of the shadow cast by the rotating five-dimensional charged Einstein-Maxwell-Chern-Simons (EMCS) black holes, which is characterized by the four pa- rameters, i.e., mass, two spins, and charge, in which spin parameters are set equal. We integrate the null geodesic equations and derive an analytical formula for the shadow of five-dimensional EMCS black hole, in turn, to show that size of black hole ( 190 )