arXiv subjects

Seema Satin

Publications and source records attributed to Seema Satin.

At least 19 recordsLinked to original sources

arXiv2025

A linear response relation in general relativity with applications to dense matter relativistic stars

A new formalism in general relativity with a linear response relation between perturbed Einstein tensor and the stress-energy tensor is presented. Basic concepts are borrowed from statistical physics and theory of stochastic processes by extending them for a spacetime structure. We show qualitatively new results of the first applications which lay foundations for a sub-hydro mesoscopic theory in dense matter relativistic stars. This will enable one to probe structure and phenomena at intermediate scales in relativistic stars and exotic fluids that they are made up of. The overall aim is to build foundations for studying dynamical equilibrium and non-equilibrium properties of astrophysical bodies based on stochastic correlations of perturbations of spacetime and matter fields. This will add to the present literature on asteroseismology a new insight in a significant way.It is also expected that this will lead to direct or indirect observational consequences of meso scale physics under extreme conditions present in the exotic objects.

gr-qc↗

arXiv2024

The hydrodynamic approximation of the semiclassical dissipation kernel in stochastic gravity

Semiclassical stochastic gravity is aimed at studying extended structure formation in the early universe. Rigorous developments in this area include the semiclassical noise and dissipation kernels which are obtained in terms of quantum stress energy tensor composed of scalar fields. The present article forms an important step in an effort to extend the theory in the decoherence limit and hydrodynamic approximation of the scalar fields. Such extensions will make it possible to analyse the extended structure formation around the decoherence era of the inflaton field in cosmology. On the other hand, modelling dissipation in fluids and effective fluids is a challenge and long standing mathematical physics related hurdles have posed difficulties for progress in this direction.The present article marks the beginning of a new way to model dissipation in an effective fluid using the widely accepted correspondence between the semiclassical fields and effective fluid approximation. A similar approach has been recently carried out for noise (fluctuations) kernel correspondence between the two, we now touch upon dissipation in the relativistic effective fluids.

gr-qc↗

arXiv2024

Perturbations in dense matter relativistic stars induced by internal sources

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.

astro-ph.HE↗

arXiv2023

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

A linear response relation between metric and fluid perturbations driven by a background noise source is used as a framework for obtaining non-radial polar perturbations in dense matter relativistic stars. The perturbations carry a generalized stochastic nature as solutions to the classical Einstein-Langevin equation which has been recently proposed. The significance of these stochastic non-radial polar perturbations lies at probing the intermediate sub-hydro scales inside the dense fluid. This study extends towards a non-equilibrium/near-equilibrium statistical mechanics study for relativistic star interiors. We address the non-radial polar perturbations in stars which are important from the point of view of detection in future. A generalized stochastic noise which originates as the remnant of collapse mechanism in isolated star is expected to give rise to such stochastic polar perturbations at intermediate sub-hydro scales. More specifically it is the interplay between the degeneracy pressure of exotic matter and the gravitational pressure that gives rise to the seeds of stochastic effects or noise in the background of the gravitating body towards the near-equilibrium configuration.

gr-qc↗

arXiv2022

Correspondences between scalar field and fluid fluctuations in curved spacetime

A correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical foundations in this area. The intention for such developments is to explore sub-hydro range mesoscopic physics for the relativistic fluids in curved spacetime. The fluid correspondences fall in the classical domain and can replace the quantum fields and fluctuations for scales around the hydrodynamic limits.The present article extends our earlier results with a more elaborate physical insight towards the quantum fluids and retention of partial quantum nature in a stochastic description in bulk of the fluids. This also accounts for non-thermal effects along with thermal and quantum fluctuations for the fields in the hydro limit. Hence the expressions presented here are very general in nature for various applications. The further scope of research that such developments give is discussed in the concluding section.

gr-qc↗

arXiv2022

A Linear Response relation for perturbations in compact stars and the classical Einstein-Langevin formalism

We give a linear response relation for perturbations in relativistic stars and classify them in terms of implicit and induced perturbations. The focus in this article is on the induced perturbations which may arise due to internal sources in dense matter compact objects. Based on the linear response relation, an Einstein Langevin equation is given and its solutions for a simple case are obtained in closed analytical form as a first exercise. Our results show how perturbations in relativistic stars can arise due to a cumulative effect of mesoscopic scale fluctuations in the dense matter fluids, which otherwise seem to be screened off at hydrodynamic scales due to averaging. We discuss the relevance of such a framework and its potential towards building up a theme of research in asteroseismology using a first principles approach.

gr-qc↗

arXiv2022

Formalism for stochastic perturbations and analysis in relativistic stars

Perturbed Einstein's equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out . These perturbations which are stochastic in nature, are of significance for building a non-equilibrium statistical theory in connections with relativistic astrophysics. A fluctuation dissipation relation for a spherically symmetric star in its simplest form is obtained. The FD relation shows how the random velocity fluctuations in the background of the unperturbed star can dissipate into Lagrangian displacement of fluid trajectories of the dense matter. Interestingly in a simple way, a constant (in time) coefficient of dissipation is obtained without a delta correlated noise. This formalism is also extended for perturbed TOV equations which have a stochastic contribution, and show up in terms of the effective or root mean square pressure perturbations. Such contributions can shed light on new ways of analysing the equation of state for dense matter. One may obtain contributions of first and second order in the equation of state using this stochastic approach.

gr-qc↗

arXiv2021

Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime-II

A correspondence between fluctuations of non-minimally coupled scalar fields and that of an effective fluid with heat flux and anisotropic stresses, is shown. Though the correspondence between respective stress tensors of scalar fields and fluids is known and widely used in literature, the fluctuations in the two cases still await a formal correspondence and are open to investigation in all details. Using results obtained in the newly established theory of semiclassical stochastic gravity which focuses on the fluctuations of the quantum stress tensor, we show new relations in this regard. This development is expected to give insight to the mesoscopic phenomena for gravitating systems, and enable backreaction studies of the fluctuations on the perturbations of astrophysical objects. Such a development is aimed to enhance the perturbative analysis for cosmological spacetimes and astrophysical objects specifically in the decoherence limit. A kinetic theory, which can be based on stochastic fluctuations vs particle picture in curved spacetime may find useful insights from such correspondences in future work.

gr-qc↗

arXiv2020

Adiabatic index for relativistic stars as a coefficient of non-thermal dissipation

The adiabatic index of a relativistic star (modeled by a perfect fluid) is shown to act as a dissipation constant due to considerations of mesoscopic scale stochastic effects. This dissipative effect arises without taking heat flux in the fluid model and is termed as adiabatic or non-thermal for the system under consideration. A basic formalism for introducing stochastic effects in interiors of massive stars has recently been proposed via a classical Einstein-Langevin equation. The origin of stochasticity is associated with the pressure variable (due to degeneracy of constituent particles ) and its fluctuations,and is not viable for pressureless fluids. The fluctuations dissipate their fermi energy into perturbing the system, adiabatically. This is shown by a fluctuation dissipation relation, and a Langevin fermi temperature associated with these fluctuations is defined.The high magnitude of background field fluctuations which we get here, is feasible to account for perturbing the strong gravity regions with dense matter. Nevertheless, the perturbations themselves are consistently and reasonably small as first order deviations from equilibrium.

gr-qc↗

arXiv2020

A Fluctuation Dissipation Relation for Relativistic stars

A fluctuation-dissipation relation for perturbed configuration of a relativistic star is obtained. The stochastic fluctuations of the classical stress tensor comprising the matter content ( a perfect fluid) of the relativistic star, act as the source in a classical Einstien-Langevin equation describing the system. We discuss the linear response of these fluctuations of the stress tensor and develop a fluctuation-dissipation relation from the first principles. Thus a system-bath separation in terms of spacetime metric and matter content is proposed, to study equilibrium and non equilibrium statistical properties for a relativistic star. This is not derived from or related to the scalar fields or quantum stress tensors and their fluctuations, as is usually the case for semiclassical stochastic gravity.

gr-qc↗

arXiv2019

Stochastic metric perturbations (radial) in gravitationally collapsing spherically symmetric relativistic star

Stochastic perturbations (radial) of a spherically symmetric relativistic star, modeled by a perfect fluid in comoving coordinates for the collapse scenario are worked out using the classical Einstein- Langevin equation, which has been proposed recently. The solutions are in terms of perturbed metric potentials and their two point correlation. For the case worked out here, it is interesting to note that the two perturbed metric potentials have same magnitude, while the potentials themselves are in general independent of each other. Such a treatment is useful for building up basic theory of non-equilibrium and near equilibrium statistical physics for collapsing stars, which should be of interest towards the end states of collapse. Here we discuss the first simple model, that of non-rotating spherically symmetric dynamically collapsing relativistic star. This paves way to further research on rotating collapse models of isolated as well as binary configurations on similar lines . Both the radial and non-radial perturbations with stochastic effects would be of interest to asteroseismology, which encompassed the future plan of study.

gr-qc↗

arXiv2018

Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime

A correspondence between fluctuations of conformally invariant quantum fields and that of classical fields finally reducing to perfect fluid matter content is shown to exist. Previously a similar correspondence between the stress tensors was known and well established in the 70's. Using recent results obtained in semiclassical stochastic gravity regarding exact definition and significance given to quantum fluctuations of the stress tensor, we obtain this correspondence, which is fundamental to statistical analysis of systems in curved spacetime. This is of immense importance, in that the fluctuations of stress tensor play a similar central role in stochastic gravity, as that of the stress tensor in classical and semiclassical gravity. A relation between the semiclassical and classical fluctuations therefore, gives insight to the mesoscopic phenomena for gravitating systems and would further enhance the perturbative analysis for cosmological spacetime and astrophysical objects, which is an expansive area of research. Interestingly we see that the quantum fluctuations have a correspondence with covaiances of pressure and density of the gravitating system in the stochastic analysis.

gr-qc↗

arXiv2018

Classical Einstein-Langevin Equation and Proposed Applications

We propose to formulate a theory for Classical Stochastic Gravity for certain applications in Astrophysics and Cosmology.This involves the Langevin approach in curved spacetime, which is introduced here, in the form of a classical Einstein-Langevin equation.The domain of applications of such an approach and possible outcomes of this formulation which are quite different than its semiclassical counterpart (which is an active area of research), are discussed.This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity and related issues in Thermodynamics. A brief calculation, to demonstrate the contribution of stochasticty and induce fluctuations to the background spacetime via heuristic solution of the Einstein Langevin equation is given .The applicability of the proposed theme can have a wider expanse than is mentioned in this article.

gr-qc↗

arXiv2017

Induced Perturbations and Stochastic effects in Collapsing Relativistic Stars

We present a modified model for relativistic stars which are usually represented by perfect fluids. Fluctuations of the stress tensor act as source in the modified Einstein's equation, giving it a Langevin equation form. The occurrence of these fluctuations is attributed to the microphysics of the interior of the star and their contribution to statistical properties of the fluid and the induced metric perturbations are argued to be of significance. We also discuss the response of fluctuations of the stress tensor in the interior of the star and possible developments towards fluctuation-dissipation theorem issues in curved spacetime. The aim and further directions of research envisioned are discussed intermittently throughout the manuscript and towards the end.

gr-qc↗

arXiv2016

Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity

For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related spacetime is known. For example, from the Minkowski solution of Martin and Verdaguer, those of the Einstein-Langevin equations in conformally-flat spacetimes, especially for spatially-flat Friedmann-Robertson-Walker models, can be readily obtained.

gr-qc↗

arXiv2016

Genericity aspects of black hole formation in the collapse of spherically symmetric slightly inhomogeneous perfect fluids

We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.

gr-qc↗

arXiv2016

Noise Kernel for Reissner Nordstrom Metric: Results at Cauchy Horizon

We obtain point separated Noise Kernel for the Reissner Nordström metric.The Noise Kernel defines the fluctuations of the quantum stress tensor and is of central importance to Semiclassical Stochastic Gravity.The metric is modeled as gravitationally collapsing spacetime, by using suitable coordinate transformations, defined earlier. The fluctuations of the quantum stress tensor, at the final stage of collapse are then analysed for both, the naked singularity and black hole end states. The behavior of this Noise Kernel, at the Cauchy Horizon for naked singularity shows markedly different behaviour from self similar Tolman Bondi metric, which was obtained earlier. In the latter a very unique divergence was seen, which does not appear for the Reissner Nordström metric, here . It is known that the quantum stress tensor itself, diverges at the Cauchy Horizon (CH) for both of these metrics . In contrast, it can now be seen that the the fluctuations of the stress tensor behave differently for the two cases. We give a discussion and further directions for investigations of this interesting behaviour in the two cases (regarding the collapse scenario).

gr-qc↗

arXiv2014

Langevin Equation on Fractal Curves

We analyse a random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, hence plays an important role in this analysis. A Langevin equation with a particular noise model is thus proposed and solved using techniques of the newly developed $F^α$-Calculus .

math-ph↗