Gravitational plane wave
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Gravitational plane waves are described as "non-flat solutions of Albert Einstein’s empty spacetime field equation".[1][2][3][4] They are a special class of a vacuum pp-wave spacetime.
In general relativity,[5] the may be defined in terms of Brinkmann coordinates by
![{\displaystyle ds^{2}=[a(u)(x^{2}-y^{2})+2b(u)xy]du^{2}+2dudv+dx^{2}+dy^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a222a809d795f518ad1e13bf32f91d33d907e699)
Here, can be any smooth functions; they control the waveform of the two possible polarization modes of gravitational radiation. In this context, these two modes are usually called the plus mode and cross mode, respectively.
See also
[edit]References
[edit]- ^ "Gravitational waves in general relativity III. Exact plane waves". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 251 (1267): 519–533. 1959-06-23. doi:10.1098/rspa.1959.0124. ISSN 0080-4630.
- ^ Russo, Jorge G. (2018). "Exact gravitational plane waves and two-dimensional gravity". Physics Letters B. 784. Elsevier BV: 142–145. doi:10.1016/j.physletb.2018.07.039. ISSN 0370-2693.
- ^ Hogan, P. A. (1980). "Plane Gravitational Waves". Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences. 80A (1). Royal Irish Academy: 85–92. ISSN 0035-8975. JSTOR 20489085. Retrieved 2024-12-23.
- ^ Wang, Anzhong (2020). Interacting Gravitational, Electromagnetic, Neutrino and Other Waves: In the Context of Einstein's General Theory of Relativity. WORLD SCIENTIFIC. doi:10.1142/9789811211492_0002. ISBN 978-981-12-1148-5.
- ^ BONDI, H. (1957). "Plane Gravitational Waves in General Relativity". Nature. 179 (4569). Springer Science and Business Media LLC: 1072–1073. doi:10.1038/1791072a0. ISSN 0028-0836.
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