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Pseudo-complex General Relativity

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Pseudo-Complex General Relativity

Part of the book series: FIAS Interdisciplinary Science Series ((FIAS))

Abstract

The history of of attempts to algebraically extend General Relativity is reviewed. The philosophy of the pseudo-complex extension is introduced and the basic assumptions, including for example a generalized variational principle and how to map to real observables. The appearance of a minimal length and the advantages of the pseudo-complex theory are discussed.

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References

  1. M.A. Abramowicz, W. Klu, No observational proof of the black-hole event horizon. A&A 396, L31 (2002)

    Article  ADS  MATH  Google Scholar 

  2. A. Einstein, A generalization of the relativistic theory of gravitation. Ann. Math. Second Ser. 46, 578 (1945)

    Google Scholar 

  3. A. Einstein, A generalized theory of gravitation. Rev. Mod. Phys. 20, 35 (1948)

    Article  ADS  MathSciNet  Google Scholar 

  4. M. Born, A suggestion for unifying quantum theory and relativity. Proc. Roy. Soc. A 165, 291 (1938)

    Article  ADS  MATH  Google Scholar 

  5. M. Born, Reprocity theory of elementary particles. Rev. Mod. Phys. 21, 463 (1949)

    Article  ADS  MATH  Google Scholar 

  6. E.R. Caianiello, Is there a maximal acceleration? Nuovo Cim. Lett. 32, 65 (1981)

    Article  Google Scholar 

  7. S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, 1973)

    Google Scholar 

  8. R.M. Wald, General Relativity (University of Chicago Press, 1994)

    Google Scholar 

  9. G. Kunstatter, R. Yates, The geometrical structure of a complexified theory of gravitation. J. Phys. A 14, 847 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  10. V. Bozza, A. Feoli, G. Lambiase, G. Papini, G. Scarpetta, Maximal acceleration effects in Kerr space. Phys. Lett. A 283, 847 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Capozziello, A. Feoli, G. Lambiase, G. Papini, G. Scarpetta, Massive scalar particles in a modified Schwarzschild geometry. Phys. Lett. A 268, 247 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. R.G. Beil, Electrodynamics from a metric. Int. J. Theor. Phys. 26, 189 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. R.G. Beil, New class of finsler metrics. Int. J. Theor. Phys. 28, 659 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. R.G. Beil, Finsler gauge transformations and general relativity. Int. J. Theor. Phys. 31, 1025 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  15. R.G. Beil, Finsler geometry and relativistic field theory. Found. Phys. 33, 110 (2003)

    Article  MathSciNet  Google Scholar 

  16. H.E. Brandt, Maximal proper acceleration and the structure of spacetime. Found. Phys. Lett. 2, 39 (1989)

    Article  Google Scholar 

  17. H.E. Brandt, Structure of spacetime tangent bundles. Found. Phys. Lett. 4, 523 (1989)

    Article  MathSciNet  Google Scholar 

  18. H.E. Brandt, Complex spacetime tangent bundle. Found. Phys. Lett. 6, 245 (1993)

    Article  MathSciNet  Google Scholar 

  19. S.G. Low, Canonical relativistic quantum mechanics: representations of the unitary semidirect Heisenberg group, \(U(1,3) \times _S H(1,3)\). J. Math. Phys. 38, 2197 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. C.L.M. Mantz, T. Prokopec, Hermitian Gravity and Cosmology (2008). arXiv:0804.0213

  21. C.L.M. Mantz, T. Prokopec, Resolving curvature singularities in holomorphic gravity. Found. Phys. 41, 1597 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. W. Moffat, A new theory of gravitation. Phys. Rev. D 19, 3554 (1979)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. P.F. Kelly, R.B. Mann, Ghost properties of algebraically extended theories of gravitation. Class. Quantum Gravity 3, 705 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  24. W. Greiner, J. Reinhardt, Field quantization (Springer, Heidelberg, 1993)

    MATH  Google Scholar 

  25. R. Adler, M. Bazin, M. Schiffer, Introduction to General Relativity, 2nd edn. (McGraw Hill, New York, 1975)

    MATH  Google Scholar 

  26. S. Carroll, Spacetime and Geometry. An Introduction to General Relativity (Addison-Wesley, San Francisco, 2004)

    MATH  Google Scholar 

  27. P.O. Hess, W. Greiner, Pseudo-complex field theory. Int. J. Mod. Phys. E 16, 1643 (2007)

    Article  ADS  Google Scholar 

  28. C. Barceló, S. Liberati, S. Sonego, M. Visser, Fate of gravitational collapse in semiclassical gravity. Phys. Rev. D 77, 044032 (2008)

    Article  ADS  Google Scholar 

  29. M. Visser, Gravitational vacuum polarization I: energy conditions in the Hartle-Hawking vacuum. Phys. Rev. D 54, 5103 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  30. M. Visser, Gravitational vacuum polarization II: energy conditions in the Bouleware vacuum. Phys. Rev. D 54, 5116 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  31. M. Visser, Gravitational vacuum polarization IV: energy conditions in the Unruh vacuum. Phys. Rev. D 56, 936 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  32. G. Caspar, T. Schönenbach, P.O. Hess, M. Schäfer, W. Greiner, Pseudo-complex general relativity: Schwarzschild, Reissner-Nordstrøm and Kerr solutions. Int. J. Mod. Phys E. 21, 1250015 (2012)

    Article  ADS  Google Scholar 

  33. P.O. Hess, W. Greiner, Pseudo-complex general relativity. Int. J. Mod. Phys. E 18, 51 (2009)

    Article  ADS  Google Scholar 

  34. P.O. Hess, L. Maghlaoui, W. Greiner, The Robertson-Walker metric in a pseudo-complex general relativity. Int. J. Mod. Phys. E 19, 1315 (2010)

    Article  ADS  Google Scholar 

  35. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman & Co., San Francisco, 1973)

    Google Scholar 

  36. F.P. Schuller. Dirac-Born-Infeld Kinematics, Maximal Acceleration and Almost Product Manifolds. Ph.D. thesis, University of Cambridge, 2003

    Google Scholar 

  37. F.P. Schuller, M.N.R. Wohlfarth, T.W. Grimm, Pauli Villars regularization and Born Infeld kinematics. Class. Quantum Gravity 20, 4269 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. C.M. Will, The confrontation between general relativity and experiment. Living Rev. Relativ. 9, 3 (2006)

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México City, Distrito Federal, Mexico

    Peter O. Hess

  2. Frankfurt Institute for Advanced Studies, University of Frankfurt, Frankfurt am Main, Hessen, Germany

    Mirko Schäfer & Walter Greiner

Authors
  1. Peter O. Hess
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  2. Mirko Schäfer
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  3. Walter Greiner
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Correspondence to Peter O. Hess .

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© 2016 Springer International Publishing Switzerland

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Hess, P.O., Schäfer, M., Greiner, W. (2016). Pseudo-complex General Relativity. In: Pseudo-Complex General Relativity. FIAS Interdisciplinary Science Series. Springer, Cham. https://doi.org/10.1007/978-3-319-25061-8_2

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