{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:14:24Z","timestamp":1760235264995,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T00:00:00Z","timestamp":1628035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11575125","11675119"],"award-info":[{"award-number":["11575125","11675119"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018769","name":"Nankai Zhide Foundation","doi-asserted-by":"publisher","award":["no"],"award-info":[{"award-number":["no"]}],"id":[{"id":"10.13039\/501100018769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Gravitational waves are regarded as linear waves in the weak field approximation, which ignores the spacetime singularity. In this paper, we analyze singularities in exact gravitational wave solutions. We provide an exact general solution of the gravitational wave with cylindrical symmetry. The general solution includes some known cylindrical wave solutions as special cases. We show that there are two kinds of singularities in the cylindrical gravitational wave solution. The first kind of singularity corresponds to a singular source. The second kind of singularity corresponds to a resonance between different gravitational waves. When two gravitational waves coexist, the interference term in the source may vanish in the sense of time averaging.<\/jats:p>","DOI":"10.3390\/sym13081425","type":"journal-article","created":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T08:47:52Z","timestamp":1628066872000},"page":"1425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Cylindrical Gravitational Wave: Source and Resonance"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6329-4083","authenticated-orcid":false,"given":"Yu-Zhu","family":"Chen","sequence":"first","affiliation":[{"name":"Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China"},{"name":"Department of Physics, Tianjin University, Tianjin 300350, China"}]},{"given":"Shi-Lin","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Physics, Tianjin University, Tianjin 300350, China"}]},{"given":"Yu-Jie","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Physics, Tianjin University, Tianjin 300350, China"}]},{"given":"Wu-Sheng","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Physics, Tianjin University, Tianjin 300350, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hawking, S.W., and Ellis, G.F.R. 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