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Deformation quantization and noncommutative black holes

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This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23–27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with Chaichian, Tureanu, Sun, Wang, Xie and Zhang.

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References

  1. Aschieri P, Blohmann C, Dimitrijevic M, et al. A gravity theory on noncommutative spaces. Class Quant Grav, 2005, 22: 3511–3532

    Article  MathSciNet  MATH  Google Scholar 

  2. Aschieri P, Dimitrijevic M, Meyer F, et al. Noncommutative geometry and gravity. Class Quant Grav, 2006, 23: 1883–1912

    Article  MathSciNet  MATH  Google Scholar 

  3. Álvarez-Gaumé L, Meyer F, Vazquez-Mozo M A. Comments on noncommutative gravity. Nucl Phys B, 2006, 753: 92–117

    Article  MATH  Google Scholar 

  4. Bayen F, Flato M, Fronsdal C, et al. Quantum mechanics as a deformation of classical mechanics. Lett Math Phys, 1977, 1: 521–530

    Article  MathSciNet  Google Scholar 

  5. Brinkmann H W. Einstein spaces which are mapped conformally on each other. Math Ann, 1925, 94: 119–145

    Article  MathSciNet  MATH  Google Scholar 

  6. Chaichian M, Demicheva A, Presnajder P, et al. Noncommutative quantum field theory: unitarity and discrete time. Phys Lett, 2001, 515: 426–430

    MATH  Google Scholar 

  7. Chaichian M, Tureanu A, Zet G. Corrections to Schwarzschild solution in noncommutative gauge theory of gravity. Phys Lett B, 2008, 660: 573–578

    Article  MathSciNet  Google Scholar 

  8. Chaichian M, Tureanu A, Zhang R B, et al. Riemannian geometry of noncommutative surfaces. J Math Phys, 2008, 49: 073511

    Article  MathSciNet  Google Scholar 

  9. Chamseddine A H. Complexified gravity in noncommutative spaces. Commun Math Phys, 2001, 218: 283–292

    Article  MathSciNet  MATH  Google Scholar 

  10. Collinson C D. Embeddings of the plane-fronted waves and other space-times. J Math Phys, 1968, 9: 403–410

    Article  MATH  Google Scholar 

  11. Ehlers J, Kundt W. Exact solutions of the gravitational field equations. In: Gravitation: An Introduction to Current Research. New York-London: John Wiley Sons, Inc, 1962, 49–101

    Google Scholar 

  12. Einstein A, Rosen N. On gravitational waves. J Franklin Inst, 1937, 223: 43–54

    Article  Google Scholar 

  13. Oppenheimer J R, Snyder H. On continued gravitational contraction. Phys Rev, 1993, 56: 455–459

    Article  Google Scholar 

  14. Pavšič M, Tapia V. Resource letter on geometrical results for embeddings and branes. arXiv: gr-qc/0010045v1, 2000

  15. Rosen J. Embedding of various relativistic Riemannian spaces in pseudo-Euclidean spaces. Rev Modern Phys, 1965, 37: 204–214

    Article  MathSciNet  MATH  Google Scholar 

  16. Seiberg N, Witten E. String theory and noncommutative geometry. J High Energy Phys, 1999, 9: 032

    Article  MathSciNet  Google Scholar 

  17. Snyder H S. Quantized space-time. Phys Rev, 1947, 71: 38–41

    Article  MATH  Google Scholar 

  18. Sun W, Wang D, Xie N, et al. Gravitational collapse of spherically symmetric stars in noncommutative general relativity. Eur Phys J C, 2010, 69: 271–279

    Article  Google Scholar 

  19. Wang D, Zhang R B, Zhang X. Quantum deformations of Schwarzschild and Schwarzschild-de sitter spacetimes. Class Quant Grav, 2009, 26: 085014

    Article  Google Scholar 

  20. Wang D, Zhang R B, Zhang X. Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves. Eur Phys J C, 2009, 64: 439–444

    Article  MATH  Google Scholar 

  21. Yang C N. On quantized space-time. Phys Rev, 1947, 72: 874

    Article  Google Scholar 

  22. Zhang R B, Zhang X. Projective module description of embedded noncommutative spaces. Rev Math Phys, 2010, 22, 507–531

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Xiao Zhang.

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Dedicated to Professor Richard V. Kadison’s 85th Birthday

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Zhang, X. Deformation quantization and noncommutative black holes. Sci. China Math. 54, 2501–2508 (2011). https://doi.org/10.1007/s11425-011-4230-9

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  • DOI: https://doi.org/10.1007/s11425-011-4230-9

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