{"title":"Schwarzschild背景下自旋场的Price定律","authors":"Siyuan Ma, Lin Zhang","doi":"10.1007/s40818-022-00139-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, we derive the globally precise late-time asymptotics for the spin-<span>\\({\\mathfrak {s}}\\)</span> fields on a Schwarzschild background, including the scalar field <span>\\(({\\mathfrak {s}}=0)\\)</span>, the Maxwell field <span>\\(({\\mathfrak {s}}=\\pm 1)\\)</span> and the linearized gravity <span>\\(({\\mathfrak {s}}=\\pm 2)\\)</span>. The conjectured Price’s law in the physics literature which predicts the sharp rates of decay of the spin <span>\\(s=\\pm {\\mathfrak {s}}\\)</span> components towards the future null infinity as well as in a compact region is shown. Further, we confirm the heuristic claim by Barack and Ori that the spin <span>\\(+1, +2\\)</span> components have an extra power of decay at the event horizon than the conjectured Price’s law. The asymptotics are derived via a unified, detailed analysis of the Teukolsky master equation that is satisfied by all these components.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-022-00139-0.pdf","citationCount":"7","resultStr":"{\"title\":\"Price’s Law for Spin Fields on a Schwarzschild Background\",\"authors\":\"Siyuan Ma, Lin Zhang\",\"doi\":\"10.1007/s40818-022-00139-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work, we derive the globally precise late-time asymptotics for the spin-<span>\\\\({\\\\mathfrak {s}}\\\\)</span> fields on a Schwarzschild background, including the scalar field <span>\\\\(({\\\\mathfrak {s}}=0)\\\\)</span>, the Maxwell field <span>\\\\(({\\\\mathfrak {s}}=\\\\pm 1)\\\\)</span> and the linearized gravity <span>\\\\(({\\\\mathfrak {s}}=\\\\pm 2)\\\\)</span>. The conjectured Price’s law in the physics literature which predicts the sharp rates of decay of the spin <span>\\\\(s=\\\\pm {\\\\mathfrak {s}}\\\\)</span> components towards the future null infinity as well as in a compact region is shown. Further, we confirm the heuristic claim by Barack and Ori that the spin <span>\\\\(+1, +2\\\\)</span> components have an extra power of decay at the event horizon than the conjectured Price’s law. The asymptotics are derived via a unified, detailed analysis of the Teukolsky master equation that is satisfied by all these components.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2022-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40818-022-00139-0.pdf\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-022-00139-0\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-022-00139-0","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Price’s Law for Spin Fields on a Schwarzschild Background
In this work, we derive the globally precise late-time asymptotics for the spin-\({\mathfrak {s}}\) fields on a Schwarzschild background, including the scalar field \(({\mathfrak {s}}=0)\), the Maxwell field \(({\mathfrak {s}}=\pm 1)\) and the linearized gravity \(({\mathfrak {s}}=\pm 2)\). The conjectured Price’s law in the physics literature which predicts the sharp rates of decay of the spin \(s=\pm {\mathfrak {s}}\) components towards the future null infinity as well as in a compact region is shown. Further, we confirm the heuristic claim by Barack and Ori that the spin \(+1, +2\) components have an extra power of decay at the event horizon than the conjectured Price’s law. The asymptotics are derived via a unified, detailed analysis of the Teukolsky master equation that is satisfied by all these components.