arXiv subjects
Publications and source records attributed to Debabrata Ghorai.
The ratio of the shear viscosity to the entropy density is calculated for non-extremal Gauss-Bonnet (GB) black holes coupled to Born-Infeld (BI) electrodynamics in $5$ dimensions. The result is found to get corrections from the BI parameter and is analytically exact upto all orders in this parameter. The computations are then extended to $D$ dimensions.
We analytically obtain the free energy and thermodynamic geometry of holographic superconductors in $2+1$-dimensions. The gravitational theory in the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the $3+1$-dimensions and is that of a charged $AdS$ black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.
The Sturm-Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that higher the value of noncommutative parameter and Born-Infeld parameter make the condensate harder to form. We also observe that the critical temperature depends on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.
In this paper, we analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics taking into account the backreaction of the spacetime using the Sturm-Liouville eigenvalue method. In the background of pure Einstein and Gauss-Bonnet gravity, based on a perturbative approach, we obtain the relation between the critical temperature and the charge density. Higher value of the backreaction and Born-Infeld parameters result in a harder condensation to form in both cases. The analytical results are found to agree with the existing numerical results. We also derive an expression for the condensation operator in $d$-dimensions which yields the critical exponent to be $1/2$.