Second-Order Effects in Gravitational Wave Spacetime
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915272724578304 |
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| author | Misyura, M. A. |
| author_facet | Misyura, M. A. |
| contents | In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and both timelike and null geodesic congruences are analyzed. For the timelike congruence, a non-vanishing expansion scalar and shear tensor are obtained, while the rotation tensor is found to vanish. In contrast, all these quantities vanish for the null congruence. Using a parallel-transported orthonormal tetrad, we derive the geodesic deviation equations up to second order in the wave amplitude $H$, showing that, as in the linear case, stretching and compression occur in the transverse $x$ and $y$ directions. However, when solving the geodesic equations numerically within the 3+1 formalism, we observe an additional effect: test particles undergo a small, second-order displacement along the direction of wave propagation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_01878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Second-Order Effects in Gravitational Wave Spacetime Misyura, M. A. General Relativity and Quantum Cosmology In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and both timelike and null geodesic congruences are analyzed. For the timelike congruence, a non-vanishing expansion scalar and shear tensor are obtained, while the rotation tensor is found to vanish. In contrast, all these quantities vanish for the null congruence. Using a parallel-transported orthonormal tetrad, we derive the geodesic deviation equations up to second order in the wave amplitude $H$, showing that, as in the linear case, stretching and compression occur in the transverse $x$ and $y$ directions. However, when solving the geodesic equations numerically within the 3+1 formalism, we observe an additional effect: test particles undergo a small, second-order displacement along the direction of wave propagation. |
| title | Second-Order Effects in Gravitational Wave Spacetime |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.01878 |