Linear perturbations of an exact gravitational wave in the Bianchi IV universe
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910160162652160 |
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| author | Osetrin, Konstantin |
| author_facet | Osetrin, Konstantin |
| contents | The proper-time method for constructing perturbative dynamical gravitational fields is presented. Using the proper-time method, a perturbative analytical model of gravitational waves against the backdrop of an exact wave solution of Einstein's equations in a Bianchi IV universe is constructed. To construct the perturbative analytical wave model a privileged wave coordinate system and a synchronous time function associated with the proper time of an observer freely moving in a gravitational wave were used. Reduction of the field equations, taking into account compatibility conditions, reduces the mathematical model of gravitational waves to a system of coupled ordinary differential equations for functions of the wave variable. Analytical solutions for the components of the gravitational-wave metric have been found. The stability of the resulting perturbative solutions is proven. The stability of the exact solution for a gravitational wave in the anisotropic Bianchi IV universe is demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03212 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear perturbations of an exact gravitational wave in the Bianchi IV universe Osetrin, Konstantin General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 83C35 The proper-time method for constructing perturbative dynamical gravitational fields is presented. Using the proper-time method, a perturbative analytical model of gravitational waves against the backdrop of an exact wave solution of Einstein's equations in a Bianchi IV universe is constructed. To construct the perturbative analytical wave model a privileged wave coordinate system and a synchronous time function associated with the proper time of an observer freely moving in a gravitational wave were used. Reduction of the field equations, taking into account compatibility conditions, reduces the mathematical model of gravitational waves to a system of coupled ordinary differential equations for functions of the wave variable. Analytical solutions for the components of the gravitational-wave metric have been found. The stability of the resulting perturbative solutions is proven. The stability of the exact solution for a gravitational wave in the anisotropic Bianchi IV universe is demonstrated. |
| title | Linear perturbations of an exact gravitational wave in the Bianchi IV universe |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 83C35 |
| url | https://arxiv.org/abs/2602.03212 |