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Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved space\u2013time. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented. <\/jats:p>","DOI":"10.1142\/s0217751x13400186","type":"journal-article","created":{"date-parts":[[2013,9,19]],"date-time":"2013-09-19T03:25:50Z","timestamp":1379561150000},"page":"1340018","source":"Crossref","is-referenced-by-count":199,"title":["ADVANCED METHODS IN BLACK-HOLE PERTURBATION THEORY"],"prefix":"10.1142","volume":"28","author":[{"given":"PAOLO","family":"PANI","sequence":"first","affiliation":[{"name":"CENTRA, Departamento de F\u00edsica, Instituto Superior T\u00e9cnico, Universidade T\u00e9cnica de Lisboa \u2013 UTL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal"},{"name":"Institute for Theory &amp; Computation, Harvard-Smithsonian CfA, 60 Garden Street, Cambridge, MA, USA"}]}],"member":"219","published-online":{"date-parts":[[2013,9,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/16\/12\/201"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.12942\/lrr-1999-2"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10714-007-0585-1"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/26\/16\/163001"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.83.793"},{"key":"rf9","volume-title":"The Mathematical Theory of Black Holes","author":"Chandrasekhar S.","year":"1992"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.081103"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.099001"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.81.104035"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.80.111701"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.241103"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.81.123530"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.241101"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/30\/15\/152001"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.88.023514"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/26\/22\/224002"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2012-12067-1"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.76.084001"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.85.044043"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1086\/153180"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/30\/4\/045011"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.22.2323"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.109.131102"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1985.0119"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.5344"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.41.2986"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.71.124008"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.76.104033"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.86.104017"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1086\/150259"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1992.0051"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.79.101501"},{"key":"rf37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.62.024027"},{"key":"rf38","first-page":"055","volume":"1106","author":"Delsate T.","journal-title":"J. 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