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Register a new userLukash plane waves, revisited
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The Lukash metric is a homogeneous gravitational wave which at late times approximates the behaviour of a generic class of spatially homogenous cosmological models with monotonically decreasing energy density. The transcription from Brinkmann to Baldwin-Jeffery-Rosen (BJR) to Bianchi coordinates is presented and the relation to a Sturm-Liouville equation is explained. The 6-parameter isometry group is derived. In the Bianchi VII range of parameters we have two BJR transciptions. However using either of them induces a mere relabeling of the geodesics and isometries. Following pioneering work of Siklos, we provide a self-contained account of the geometry and global structure of the spacetime. The latter contains a Killing horizon to the future of which the spacetime resembles an anisotropic version of the Milne cosmology and to the past of which it resemble the Rindler wedge.
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We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einsteins vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zeldovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the velocity memory effect, considered by Braginsky, Thorne, Grishchuk, and Polnarev.
The gravitational memory effect due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midi-superspace quantization is given.
We revisit the two-field mimetic gravity model with shift symmetries recently proposed in the literature, especially the problems of degrees of freedom and stabilities. We first study the model at the linear cosmological perturbation level by quadratic Lagrangian and Hamiltonian formulations. We show that there are actually two (instead of one) scalar degrees of freedom in this model in addition to two tensor modes. We then push on the study to the full non-linear level in terms of the Hamiltonian analysis, and confirm our result from the linear perturbation theory. We also consider the case where the kinetic terms of the two mimetic scalar fields have opposite signs in the constraint equation. We point out that in this case the model always suffers from the ghost instability problem.
We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of the future space-based observations.
We consider the gravitational radiation in conformal gravity theory. We perturb the metric from flat Mikowski space and obtain the wave equation after introducing the appropriate transformation for perturbation. We derive the effective energy-momentum tensor for the gravitational radiation, which can be used to determine the energy carried by gravitational waves.
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