Induced polar perturbations with stochastic effects in dense matter relativistic stars: A theoretical probe at intermediate sub-hydro mesoscopic scales

Abstract

A linear response relation between metric and fluid perturbations driven by a background internal noise source is used as a framework for addressing stochastic effects in order to establish a mesoscopic theory for dense matter relativistic stars. In this paper, nonradial polar perturbations are worked out, which are important from the point of view of detection in future. We present qualitative first results in this paper, numerical estimates have to await further progress in theoretical modeling. These perturbations carry a new generalized stochastic nature and are obtained as solutions of the classical Einstein–Langevin equation which has been recently proposed. The significance of these stochastic nonradial polar perturbations lies at probing the intermediate sub-hydro scales inside the dense fluid. This formalism extends towards a mesoscopic scale nonequilibrium/near-equilibrium statistical mechanics study for relativistic star interiors. The generalized stochastic noise originates as the remnant of collapse mechanism and dynamical effects at intermediate scales in isolated massive stars which drives these polar perturbations. More specifically, for cold dense matter which is our focus in this paper, it is either the interplay between the degeneracy pressure and the gravitational pressure, or the multiscale phenomena like turbulences giving rise to the seeds of stochastic effects in the gravitating body. Characterizing such stochastic effects can lead to an improved understanding of the nature of dense matter and help to probe multiple scales which are yet untouched.