{"title":"The Kerr/CFT Correspondence and its Extensions","authors":"Geoffrey Compère","doi":"10.12942/lrr-2012-11","DOIUrl":null,"url":null,"abstract":"<p>We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordstr?m black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an <i>SL</i>(2, ?) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":null,"pages":null},"PeriodicalIF":26.3000,"publicationDate":"2012-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-11","citationCount":"242","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Living Reviews in Relativity","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.12942/lrr-2012-11","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 242
Abstract
We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordstr?m black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL(2, ?) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.
期刊介绍:
Living Reviews in Relativity is a peer-reviewed, platinum open-access journal that publishes reviews of research across all areas of relativity. Directed towards the scientific community at or above the graduate-student level, articles are solicited from leading authorities and provide critical assessments of current research. They offer annotated insights into key literature and describe available resources, maintaining an up-to-date suite of high-quality reviews, thus embodying the "living" aspect of the journal's title.
Serving as a valuable tool for the scientific community, Living Reviews in Relativity is often the first stop for researchers seeking information on current work in relativity. Written by experts, the reviews cite, explain, and assess the most relevant resources in a given field, evaluating existing work and suggesting areas for further research.
Attracting readers from the entire relativity community, the journal is useful for graduate students conducting literature surveys, researchers seeking the latest results in unfamiliar fields, and lecturers in need of information and visual materials for presentations at all levels.