AR_final file_2018-19

sient and persistently variable black hole sources as a function of time can be explained by variation of the Compton cloud size in a TCAF solution. Jibitesh Dutta Cosmological dynamics of brane gravity: A global dynamical system perspective The braneworld model of gravity is well-known for several notable cosmological features, such as self- acceleration originating from a geometric and not matter source, effective dark energy behaviour with phantom characteristics, but not leading to a big- rip singularity, rough resemblance to the Λ CDM evolution, etc. The dynamical system tools usu- ally allow us to obtain generic conclusions on the global dynamics of a system over a wide range of initial conditions. With this motivation, in order to recover the important features of the braneworld model from a more global perspective, here, we in- vestigate the global cosmological dynamics of the braneworld model using dynamical system tech- niques. We first analyze the case where there is just a normal matter on the brane and then ex- tend the analysis to the case with an extra scalar field also trapped on the brane. In the presence of a scalar field, potentials belonging to different classes are considered. The stability behaviour of critical points is examined using linear stability analysis and when necessary center manifold theory as well as numerical perturbation techniques are also used. To understand the global dynamics of a dynamical system, we utilized the Poincare compactification method to capture the properties of all possible critical points. Applying dynamical system anal- ysis, we found that brane gravity was consistent with observed actions of the Universe. In particu- lar, our analysis shows that important cosmological behaviours like the long-lasting matter-dominated era, late time acceleration as well as the avoidance of big-rip singularity can be realized in brane grav- ity for a wide range of initial conditions. This work has been done in collaboration with Hmar Zonun- mawia, Wompherdeiki Khyllep, and Laur Jarv. Thermodynamics of event horizon with modified Hawking temperature in scalar-tensor gravity In recent past, Hawking temperature has been modified for the validity of thermodynamical laws at the event horizon in general relativity context. This lead to the introduction of modified Hawking temperature, and it has been found that the mod- ified Hawking temperature is more realistic on the event horizon. With this motivation, here we inves- tigate the thermodynamical consistency of scalar- tensor gravity based models by examining the va- lidity of the generalized second law of thermody- namics (GSLT) and thermodynamical equilibrium (TE) at the event horizon. In order to attain our goal, we consider a spatially flat Friedman Robert- son Walker Universe filled with ordinary matter and the boundary of the Universe bounded by the event horizon that is in thermal equilibrium with modified Hawking temperature. Next, we calculate the general expressions for the GSLT and TE us- ing modified Hawking temperature in the context of the more general action of scalar-tensor grav- ity where, there is a non-minimally coupling be- tween the scalar field and matter Lagrangian (as the Chameleon field). From the general expression of GSLT, we find that the null energy condition must hold for a viable scalar-tensor model of the Universe dominated by a perfect fluid. Further- more, in order to better understand these compli- cated general expressions of GSLT and TE, we ex- plore the validity of the GSLT and TE for two vi- able models of scalar-tensor gravity namely Brans- Dicke gravity with a self-interacting potential and Chameleon gravity at the event horizon using spe- cial cosmological solutions. Finally, some graphical representation of the GSLT and TE have been pre- sented. From the graphical analysis, we found that the power-law forms of the scale factor and scalar field were much favourable for the study of univer- sal thermodynamics as compared to other choices of the scalar field and the analytic function. This work has been done in collaboration with Binod Chetry, and Asrin Abdolmaleki. Sunandan Gangopadhyay Holographic complexity for Lifshitz system The holographic complexity of a 3 + 1-dimensional Lifshitz spacetime having a scaling symmetry is computed. The change in the holographic com- plexity between the excited state and the ground state is then obtained. This is then related to the changes in the energy and the entanglement chem- ical potential of the system. The calculation is car- ried out for both the values of the dynamical scaling exponent z in the Lifshitz spacetime. The relations has a very similar form to the corresponding rela- ( 189 )