arXiv subjects

Sucheta Datta

Publications and source records attributed to Sucheta Datta.

6 recordsLinked to original sources

arXiv2023

Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes

In this paper, we study the gravitational memory effect in pp-wave spacetimes due to the passage of a pulse having the form of a ramp profile through this spacetime. We have analyzed the effect of this pulse on the evolution of nearby geodesics, and have determined analytical solutions of the geodesic equations in the Brinkmann coordinates. We have also examined the changes in the separation between a pair of geodesics and their velocity profiles. The separation (along $ x $ or $ y $-direction) increases monotonically from an initial constant value. In contrast, the relative velocity grows from zero and settles to a final non-zero constant value. These resulting changes are retained as memory after the pulse dies out. The nature of this memory is similar to that determined by earlier workers using Gaussian, square, and other pulse profiles, thereby validating the universality of gravitational wave memory.

gr-qc↗

arXiv2023

Memory Effect of Plane Gravitational Wave Pulses

A gravitational wave pulse, while passing through spacetime, brings about a change in the relative separation between free particles. This `memory effect' serves as one of the signatures of gravitational waves. In this paper, we consider some viable pulse profiles which are not yet analyzed by others (e.g., $u^{-4}$, $u^{-2}$, $ \frac{c}{(u^2 + au +b)^2} $), and examine the memory effect produced by these wave pulses in pp-wave spacetime. We choose to work in the Brinkmann coordinates to solve the geodesic equations. From the plots of the corresponding analytical solutions, we observe a non-zero separation between a pair of geodesics in each case, after the pulse dies out. The displacement memory effect either increases or decreases monotonically, whereas the velocity memory effect reaches saturation after an initial rise or drop.

gr-qc↗

arXiv2022

On the propagation of gravitational waves in matter-filled Bianchi I universe

In this paper we apply the Regge-Wheeler formalism to study the propagation of axial and polar gravitational waves in matter-filled Bianchi I universe. Assuming that the expansion scalar $ \Theta $, of the background space-time, is proportional to the shear scalar $ \sigma $, we solved the background field equations in the presence of matter (found to behave like a stiff fluid). We then derive the linearised perturbation equations for both the axial and polar modes. The analytical solutions in vacuum spacetime could be determined in an earlier paper \cite{GD1} in a relatively straightforward manner. However, here we find that in the presence of matter, they require more assumptions for their solution, and bear more involved forms. As compared to the axial modes, the polar perturbation equations contain far more complicated couplings among the perturbing terms. Thus we have to apply suitable assumptions to derive the analytical solutions for some of the cases of polar perturbations. In both the axial and polar cases, the radial and temporal solutions for the perturbations separate out as products. We find that the axial waves are damped owing to the background anisotropy, and can deform only the azimuthal velocity of the fluid. In contrast, the polar waves must trigger perturbations in the energy density, the pressure as well as in the non-azimuthal components of the fluid velocity. Similar behaviour is exhibited by axial and polar gravitational waves propagating in the Kantowski-Sachs universe \cite{GD2}. Our work is in contrast to the work done in \cite{SYK}, where the authors analysed anisotropic universes modelled by Kasner spacetime and Rindler wedges using the method of gauge-invariant perturbations in the RW gauge.

gr-qc↗

arXiv2021

Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe

We apply the Regge-Wheeler formalism to study axial and polar gravitational waves in Kantowski-Sachs universe. The background field equations and the linearised perturbation equations for the modes are derived in presence of matter. To find analytical solutions, we analyze the propagation of waves in vacuum spacetime. The background field equations in absence of matter are solved by assuming the expansion scalar to be proportional to the shear scalar. Using the method of separation of variables, the axial perturbation parameter $ h_0(t, r) $ is obtained from its wave equation. The other perturbation $ h_1(t, r) $ is then determined from $ h_0(t, r) $. The anisotropy of the background spacetime is responsible for the damping of the axial waves. The polar perturbation equations are much more involved compared to their FLRW counterparts, as well as to the axial perturbations in Kantowski-Sachs background. In both the axial and polar cases, the radial and temporal solutions separate out as products. The temporal part of the polar perturbation solutions are plotted against time to obtain an order of magnitude estimate of the frequency of the propagating GWs and lies in the range 1000-2000 Hz. Using standard observational data for the GW strain we have placed constraints on the parameters in the polar perturbation solutions. The perturbation equations in presence of matter show that the axial waves can cause perturbations only in the azimuthal velocity of the fluid without deforming the matter field. But the polar waves must perturb the energy density, the pressure and also the non-azimuthal components of the fluid velocity.

gr-qc↗

arXiv2020

Axial Gravitational Waves in Bianchi I Universe

In this paper, we have studied the propagation of axial gravitational waves in Bianchi I universe using the Regge-Wheeler gauge. In this gauge, there are only two non-zero components of $ h_{μν} $ in the case of axial waves: $h_0(t,r)$ and $h_1(t,r)$. The field equations in absence of matter have been derived both for the unperturbed as well as axially perturbed metric. These field equations are solved simultaneously by assuming the expansion scalar $Θ$ to be proportional to the shear scalar $σ$ (so that $a= b^n$, where $a$, $b$ are the metric coefficients and $n$ is an arbitrary constant), and the wave equation for the perturbation parameter $h_0(t,r)$ have been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined $h_1(t,r)$. We then discuss a few special cases in order to interpret the results. We find that the anisotropy of the background spacetime is responsible for the damping of the gravitational waves as they propagate through this spacetime. The perturbations depend on the values of the angular momentum $l$. The field equations in the presence of matter reveal that the axially perturbed spacetime leads to perturbations only in the azimuthal velocity of the fluid leaving the matter field undisturbed.

gr-qc↗

arXiv2019

Propagation of Gravitational Waves in Anisotropic Universe

In this paper, we have considered a toy model of an anisotropic universe and studied the propagation of gravitational waves in such a universe. The consideration of this toy model simplifies the analysis and helps us to illustrate the effects of anisotropy. Incorporating linear perturbations on this anisotropic background, we have considered the synchronous, transverse, traceless gauge conditions and evaluated the perturbations of the Ricci tensor. The energy-momentum tensor is that of a perfect fluid, for which the Einstein's field equations are determined in presence of perturbations. We arrive at the set of linearised Einstein's equations explicitly and find solutions for gravitational waves propagating along the direction of anisotropy. We also study the propagation along a direction perpendicular to the direction of anisotropy. Subsequently we have validated the assumption of the tracelessness of the linear perturbations. Finally we determine the amount of tidal acceleration caused by the propagation of gravitational waves in this background spacetime.

gr-qc↗