{"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}
引用次数: 7
Abstract
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.