Perturbations in dense matter relativistic stars induced by internal sources

Abstract

Einstein's field equations with a background source term that induces perturbations and the applications of this new formalism to a compact dense matter relativistic star are presented. We introduce a new response kernel in the field equations between the metric and fluid perturbations. A source term which drives or induces the sub-hydro mesoscopic scales perturbations in the astrophysical system, is of importance here. Deterministic as well as stochastic perturbations for the radial case are worked out as solutions of field equations. We also touch upon polar perturbations that are deterministic with oscillatory parts. The stochastic perturbation are of significance in terms of two point or point separated correlations which form the building blocks for studying equilibrium and non-equilibrium statistical mechanics for the system. Our main aim is to build a theory for intermediate scale physics, for dense exotic matter and investigate structure of the compact astrophysical objects. Specifically, turbulence which connects various scales in superfluid matter in the dense stars is an area gaining importance. The work presented here is the starting point for new theoretical frame work that touches upon various yet unexplored scales where mechanical and dynamical effects interior to the matter of the star are of significance. Thus there is scope for extending studies in asteroseismology to mesoscopic effects at the new intermediate scales in the cold dense matter fluid . This is expected to enable us to probe astrophysical features at refined scales through theoretical formulations as well as for observational consequences.