Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies

Bradley, Michael; Forsberg, Mats; Keresztes, Zoltán

doi:10.3390/universe3040069

Cited by 17 publications

(43 citation statements)

References 69 publications

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“…In this section we derive the linearised field equations for the KS metric with polar perturbations (27) in presence of matter. The expressions for the perturbed energy-momentum tensor are available from equations ( 45)- (50). The (0-0) component in this case is different:…”

Section: Discussionmentioning

confidence: 99%

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

Datta,

Guha

2021

Preprint

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In this paper, we apply the Regge-Wheeler formalism in our study of axial and polar gravitational waves in Kantowski-Sachs universe. The background field equations and the linearised perturbation equations for axial and polar modes are derived in presence of matter. To find the analytical solutions, we analyse the propagation of waves in vacuum spacetime. The background field equations in absence of matter are first solved by assuming that the expansion scalar Θ to be proportional to the shear scalar σ (so that the metric coefficients are given by the relation a = b n , where n is an arbitrary constant). 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). We observe that the anisotropy of the background spacetime is responsible for the damping of the axial waves propagating through it. On the other hand, the polar perturbation equations are much more involved compared to their FLRW counterparts, as well as to the axial perturbations in Kantowski-Sachs background. The polar equations contain complicated couplings among the perturbation variables. In both the axial and polar cases, the radial and temporal solutions for the perturbations separate out as product. 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. The propagation of axial and polar gravitational waves in Kantowski-Sachs and Bianchi I spacetimes is found to be more or less similar in nature.

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Section: Discussionmentioning

confidence: 99%

“…Beyond the geometrical optics approximation, they have indicated the existence of direction-dependent dispersion relations. This treatment has also been extended to LRS class-II cosmologies [50].…”

Section: Introductionmentioning

confidence: 99%

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

Datta,

Guha

2021

Preprint

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“…The properties of the background spacetimes are here breifly summarized. For more details the reader is referred to [30,32,33].…”

Section: Background Spacetimesmentioning

confidence: 99%

“…In some earlier papers [29][30][31] we studied vorticity free perturbations on a class of anisotropic cosmological models, given by the homogeneous and orthogonal locally rotationally symmetric (LRS) spacetimes of class II [32,33]. The restriction to zero vorticity was partly due to the significant simplifications this implies for the commutator relations, but was also motivated by that vorticity cannot be generated in a perfect fluid with barotropic equation of state, cf.…”

Section: Introductionmentioning

confidence: 99%

General perfect fluid perturbations of homogeneous and orthogonal locally rotationally symmetric class II cosmologies

Törnkvist¹,

Bradley²

2019

Phys. Rev. D

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First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime. The perturbations, which are of perfect fluid type, include general scalar, vector and tensor modes and extend some previous works where vorticity perturbations were excluded. A harmonic decomposition is performed and the field equations are then reduced to a set of eight evolution equations for eight harmonic coefficients, representing perturbations in density, shear, vorticity and the Weyl tensor, in terms of which all other variables can be expressed algebraically. This system decouples into two sub-systems, one for five and one for three coefficients. As previously known, vorticity perturbations cannot be generated to any order in a barytopic perfect fluid. Hence the time development of existing first order vorticity perturbations are seen to be completely determined by the background. However, an already existing vorticity will act as source terms in the evolution equations for the other quantities. In the high frequency approximation the four independent Weyl tensor harmonics evolve as gravitational waves on the anisotropic background in the same manner as in the case without vorticity, whereas vorticity gives a first order disturbance of sonic waves.

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“…The gauge problem plaguing the linear perturbations in cosmological models has been addressed in several papers [29][30][31][32]. The perturbations introduced in [30] are used to study the GWs in Kantowski-Sachs [33] and locally rotationally symmetric class-II [34] cosmologies.…”

Section: Introductionmentioning

confidence: 99%

Axial Gravitational Waves in Bianchi I Universe

Guha,

Datta

2020

Preprint

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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 Bianchi I spacetime.

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Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies

Cited by 17 publications

References 69 publications

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

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

General perfect fluid perturbations of homogeneous and orthogonal locally rotationally symmetric class II cosmologies

Axial Gravitational Waves in Bianchi I Universe

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