On the universal hydrodynamics of strongly coupled CFTs with gravity duals

It is known that the solutions of pure classical 5D gravity with $AdS_5$ asymptotics can describe strongly coupled large N dynamics in a universal sector of 4D conformal gauge theories. We show that when the boundary metric is flat we can uniquely specify the solution by the boundary stress tensor. We also show that in the Fefferman-Graham coordinates all these solutions have an integer Taylor series expansion in the radial coordinate (i.e. no $log$ terms). Specifying an arbitrary stress tensor can lead to two types of pathologies, it can either destroy the asymptotic AdS boundary condition or it can produce naked singularities. We show that when solutions have no net angular momentum, all hydrodynamic stress tensors preserve the asymptotic AdS boundary condition, though they may produce naked singularities. We construct solutions corresponding to arbitrary hydrodynamic stress tensors in Fefferman-Graham coordinates using a derivative expansion. In contrast to Eddington-Finkelstein coordinates here the constraint equations simplify and at each order it is manifestly Lorentz covariant. The regularity analysis, becomes more elaborate, but we can show that there is a unique hydrodynamic stress tensor which gives us solutions free of naked singularities. In the process we write down explicit first order solutions in both Fefferman-Graham and Eddington-Finkelstein coordinates for hydrodynamic stress tensors with arbitrary $\eta/s$. Our solutions can describe arbitrary (slowly varying) velocity configurations. We point out some field-theoretic implications of our general results.Comment: 39 pages, two appendices added, in appendix A the proof of the power series solution has been detailed, in appendix B, we have commented on method of fixing $\eta/s$ by calculating curvature invariant

Charged Vaidya-Tikekar model for super compact star

In this work, we explore a class of compact charged spheres that have been tested against experimental and observational constraints with some known compact stars candidates. The study is performed by considering the self-gravitating, charged, isotropic fluids which is more pliability in solving the Einstein-Maxwell equations. In order to determine the interior geometry, we utilize the Vaidya-Tikekar geometry for the metric potential with Riessner-Nordstrom metric as an exterior solution. In this models, we determine constants after selecting some particular values of M and R, for the compact objects SAX J1808.4-3658, Her X-1 and 4U 1538-52. The most striking consequence is that hydrostatic equilibrium is maintained for different forces, and the situation is clarified by using the generalized Tolman-Oppenheimer-Volkoff (TOV) equation. In addition to this, we also present the energy conditions, speeds of sound and compactness of stars that are very much compatible to that for a physically acceptable stellar model. Arising solutions are also compared with graphical representations that provide strong evidences for more realistic and viable models, both at theoretical and astrophysical scale.Comment: 13 Pages, 5 Figures and 4 Table