Axial Gravitational Waves in Bianchi I Universe

Abstract

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 $h_{\mu \nu }$ 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 $\Theta$ to be proportional to the shear scalar $\sigma$ (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.

arXiv comment14 pages, final form accepted for publication in IJMPD

References in corpus (21)

• Analytic black hole perturbation approach to gravitational radiation
• Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism
• Theory of cosmological perturbations in an anisotropic universe
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Some Bianchi Type Cosmological Models in f(R) Gravity
• Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior
• Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects
• Perturbation Theory in Lemaitre-Tolman-Bondi Cosmology
• Propagation of Polar Gravitational Waves in f(R,T) Scenario
• Stochastic Backgrounds of Gravitational Waves from Cosmological Sources: Techniques and Applications to Preheating
• Relic gravitational waves from Quintessential Inflation
• The Huygens principle and cosmological gravitational waves in the Regge-Wheeler gauge
• Axial and polar gravitational wave equations in a de Sitter expanding universe by Laplace transform
• Gravitational waves in Friedman-Lemaitre-Robertson-Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle
• Gravitational Waves in Bianchi Type-I Universes I: The Classical Theory
• Gravitational, shear and matter waves in Kantowski-Sachs cosmologies
• Curvature-Matter Coupling Effects on Axial Gravitational Waves
• Axial gravitational waves in FLRW cosmology and memory effects
• Evolution of linear perturbations in spherically symmetric dust spacetimes
• Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies
• Primordial Gravitational Waves Spectrum in the Coupled-Scalar-Tachyon Bounce Universe

Cited by in corpus (2)

• Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe
• On the propagation of gravitational waves in matter-filled Bianchi I universe