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We refer to these conditions as conformal Killing initial data (CKID), and they extend the well-known Killing initial data (KID) that have been known for a long time. The procedure used to find the CKID is a classical argument, which is reviewed and presented in a form that may have an independent interest, based on identifying a suitable propagation identity and checking the well-posedness of the corresponding initial value problem. As example applications, we review the derivation of the KID conditions as well as give a more thorough treatment of the homothetic KID conditions than was previously available in the literature.<\/jats:p>","DOI":"10.1063\/1.5126683","type":"journal-article","created":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T15:47:09Z","timestamp":1576511229000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Conformal Killing initial data"],"prefix":"10.1063","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1165-4689","authenticated-orcid":false,"given":"Alfonso","family":"Garc\u00eda-Parrado","sequence":"first","affiliation":[{"name":"Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague 1 , V Hole\u0161ovi\u010dk\u00e1ch 2, 180 00 Praha 8, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4255-6579","authenticated-orcid":false,"given":"Igor","family":"Khavkine","sequence":"additional","affiliation":[{"name":"Institute of Mathematics of the Czech Academy of Sciences 2 , \u017ditn\u00e1 25, 115 67 Praha 1, Czech Republic"}]}],"member":"317","published-online":{"date-parts":[[2019,12,16]]},"reference":[{"key":"2023080523551081100_c1","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1007\/s00023-010-0063-2","article-title":"On the construction of a geometric invariant measuring the deviation from Kerr data","volume":"11","year":"2010","journal-title":"Ann. 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