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Geometry of Higher Dimensional Black Hole and Compact Einstein Space

Research Project

Project/Area Number 17540262
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Particle/Nuclear/Cosmic ray/Astro physics
Research InstitutionOsaka City University

Principal Investigator

YASUI Yukinori  Osaka City University, Mathematics and Physics, Associate Professor, 大学院理学研究科, 准教授 (30191117)

Co-Investigator(Kenkyū-buntansha) HASHIMOTO Yoshitake  Osaka City University, Mathematics and Physics, Associate Professor, 大学院理学研究科, 准教授 (20271182)
SAKAGUCHI Makoto  Okayama Institute for Quantum Physics, Researcher, 研究員 (90382027)
Project Period (FY) 2005 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsEinstein manifold / black hole / AdS / CFT correspondence / instanton
Research Abstract

We aimed to study compact Einstein manifolds and Riemannian manifolds of special holonomy from a view point of black hole.
These geometries are physically interpreted as higher dimensional gravitational instantons, and deeply related to new geometries expected by string theory. Especially, compact Sasaki-Einstein geometry has been extensively studied in connection with AdS/CFT correspondence.
1. We have constructed a new infinite series of Einstein metrics on sphere bundles. These metrics appear as a certain limit of 5-dimensional AdS Kerr black holes. In the special case, the metric gives a homogeneous Sasaki-Einstein metric. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on the first del Pezzo surface.
2. Recently, D3 branes at the tip of toric Calabi-Yau cones have been extensively studied from a view point of AdS/CFT correspondence. It is natural to consider the deformations of cone metrics in order to explore non-conformal field theories. We have constructed an explicit non-singular complete toric Calabi-Yau metric using the local solution found by Chen, Lu and Pope. This metric gives a new supergravity solution representing D3 branes.
3. We have constructed a new infinite family of quiver gauge theories which blow down to the quiver gauge theories found by Hannany, Kazakopoulos and Wecht, recently. This family includes a quiver gauge theory for the third del Pezzo surface. We have shown, using volume minimaization, that these theories generically have irrational R-charges. The AdS/CFT correspondence implies that the dual geometries are irregular toric Sasaki-Einstein manifolds.
4. We studied stationary and axially symmetric solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method. From five dimensional Minkowski space-time as a seed, we reproduced a black ring solution with a rotating two sphere which was found by Mishima and Iguchi recently.

Report

(3 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • Research Products

    (19 results)

All 2007 2006 2005

All Journal Article (19 results)

  • [Journal Article] New Example of Infinite Family of Quiver Gauge Theories2007

    • Author(s)
      T.Oota
    • Journal Title

      Nuclear Physics B 762

      Pages: 377-391

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Kerr-NUT de Sitter Curvature in All Dimensions2007

    • Author(s)
      N.Hamamoto
    • Journal Title

      Journal of Physics A : Mathematical and Theor et al. 40

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] New Example of Infinite Family of Quiver Gauge Theories2007

    • Author(s)
      T.Oota
    • Journal Title

      Nuclear Physiocs B 762

      Pages: 377-391

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Vacuum Solutions of Five Dimensional Einstein Equations2006

    • Author(s)
      S.Tomizawa
    • Journal Title

      Physical Review D 73

      Pages: 64009-64009

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry2006

    • Author(s)
      M.Sakaguchi
    • Journal Title

      Journal of Geometry and Physics 56

      Pages: 2463-2479

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Notes on Five-dimensional Kerr Black Holes2006

    • Author(s)
      M.Sakaguchi
    • Journal Title

      International Journal of Modern Physics A 26.11

      Pages: 2331-2352

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Explicit Toric Metric on Resolved Calabi-Yau Cone2006

    • Author(s)
      T.Oota
    • Journal Title

      Physics Letters B 639

      Pages: 54-56

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Toric Sasaki-Einstein Manifolds and Heun Equations2006

    • Author(s)
      T.Oota
    • Journal Title

      Nuclear Physics B 742

      Pages: 275-294

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 場の量子論と微分幾何学-Einstein計量と特殊ホロノミー多様体2006

    • Author(s)
      安井 幸則
    • Journal Title

      別冊・数理科学 10月号

      Pages: 156-163

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Notes on Five-dimensional Kerr Black Holes2006

    • Author(s)
      M.Sakaguchi
    • Journal Title

      International Journal of Modern Physics A 26

      Pages: 2331-2352

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Explicit Toric Mertic on Resolved Calabi-Yau Cone2006

    • Author(s)
      T.Oota
    • Journal Title

      Physics Letters B 639

      Pages: 54-56

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Einstein metric and Special Holonomy Manifold2006

    • Author(s)
      Y.Yasui
    • Journal Title

      Suurikagaku 10

      Pages: 156-163

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Seven-dimensional Einstein Manifolds fron Tod-Hitchin Geometry2006

    • Author(s)
      M.Sakaguchi
    • Journal Title

      Journal of Geometry and Physics 56

      Pages: 2463-2479

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 場の量子論と微分幾何学 Einstein計量と特殊ホロノミー多様体2006

    • Author(s)
      安井 幸則
    • Journal Title

      別冊・数理科学 10月号

      Pages: 156-163

    • Related Report
      2006 Annual Research Report
  • [Journal Article] New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes2005

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Communications in Mathematical Physics 257

      Pages: 273-285

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Scalar Laplacian on Sasaki-Einstein Manifolds Ypq2005

    • Author(s)
      H.Kihara
    • Journal Title

      Physics Letters B 621

      Pages: 288-294

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] New infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes2005

    • Author(s)
      Y.Hashimoto
    • Journal Title

      Communications in Mathematical Physics 257

      Pages: 273-285

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Scalar Laplacian on Sasaki-Einstein Manifolds Y^{p,q}2005

    • Author(s)
      H.Kihara, M.Sakaguchia, Y.Yasui
    • Journal Title

      Physics Letter B 621

      Pages: 288-294

    • Related Report
      2005 Annual Research Report
  • [Journal Article] New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes2005

    • Author(s)
      Y.Hashimoto, M.Sakaguchi, Y.Yasui
    • Journal Title

      Communications in Mathematical Physics 257

      Pages: 273-285

    • NAID

      110006414719

    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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