AR-2019-2020

help of hybrid scale factor and the proportionality of shear scalar with expansion scalar (i.e., σ ∝ θ ). We have calculated some physical and geometri- cal properties of the models and their behaviour is thoroughly studied with the help of their plots with respect to redshift (z). It is observed that for all three models, pressure ( p ) is negative and energy density ( ρ ) is positive. In case of Bianchi type V, VI 0 models, the EoS parameter exhibits quintom-like behaviour. Also, by using the same functional form, we have studied all energy condi- tions for three models. At present ( z = 0), the energy conditions particularly NEC and DEC are fulfilled, and SEC is violated for all three mod- els, which supports the accelerating expansion of the universe. The advantage of choosing this func- tional form is that it gives the asymptotically exact de Sitter solution, and also the obtained values of physical parameters matches with the current ob- servational data. This work is done in collaboration with K. Sri Kavya. Sudhaker Upadhyay Phase transition of a charged AdS black hole with a global monopole through geometrical thermodynam- ics In order to study the phase transition through thermodynamic geometry, we consider the charged AdS black hole with global monopole. We first introduce thermodynamics of charged AdS black hole with global monopole by discussing the de- pendence of Hawking temperature, specific heat and Pv curve on horizon radius and monopole pa- rameter. By implementing various thermodynamic geometry methods, for instance, Weinhold, Rup- piner, Quevedo and HPEM formulations, we de- rive corresponding scalar curvatures for charged AdS black hole with a global monopole. Here, we observe that, in contrast to Weinhold and Rup- peiner methods, HPEM and Quevedo formulations provide more information about the phase transi- tion of the charged AdS black hole with a global monopole. This work is done in collaboration with Saheb Soroushfar. Accretion disks around a static black hole in f(R) gravity We provide a description of a thin accretion disk for a static spherically symmetric black holes in f(R) gravity. In this regard, we first study the hori- zons of black holes in f(R) gravity. The equation of motion and effective potential are also computed, which eventually leads to possible existence of in- nermost circular orbits of accretion disk. We de- rive the specific energy, specific angular momen- tum and angular velocity of the particles moving in circular orbits. A comparative study of vari- ous parameters is also presented. The locations of the event horizon, cosmological horizon, inner- most and outermost stable circular orbits are also pointed out. This work is done in collaboration with Saheb Soroushfar. Murli Manohar Verma Extended galactic rotational velocity profiles in f ( R ) gravity background An attempt has been made to explore the geo- metric effects of f ( R ) action on the galactic dy- namics under the weak field approximation. The rotational velocity is calculated beyond the Ein- stein’s geometric theory of gravity. It is inspired by the cosmological geometric relation obtained in the power-law f ( R ) gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein-Hilbert gravity action (taking R as f ( R ) ∝ R 1+ δ ) at the galactic scales for the expla- nation of flatness paradox associated with the clus- tered galactic dark matter. We obtain the contri- bution of dynamical f ( R ) cosmological background geometry in accelerating the test mass. Further- more, the integrated effective acceleration of the test mass due to a massive spherically symmet- ric source in f ( R ) background is calculated via the study of geodesics for the suitable spacetime met- ric, and an equation for the effective rotational ve- locity has been developed. We test the viability of the proposed model by tracing the motion of test mass far from the disk of galactic matter for smaller δ . The possible galactic rotational velocity curves in f ( R ) background are discussed for the formula obtained with δ << 1. We also obtain constraints on δ O (10 − 6 ) confirmed by observations. This work is doen in collaboration with Vipin Kumar Sharma, and Bal Krishna Yadav. Dark matter as scalaron in f ( R ) gravity models We explore the scalar field obtained under the con- formal transformation of the spacetime metric g μν from the Jordan frame to the Einstein frame in