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Complex General Relativity

  1. Sep 1, 2009 #1

    Jim

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    Complex (not because its difficult !), but because certain elements of classical, real GR
    are allowed to assume complex (real + imag parts) values, such as the metric or connexion.
    I am wondering if anyone is aware of any legitimate work going on in this area ??
    I have already been shanghied by a crackpot's book (blaha's) only to find out that he has never published on this subject either on arxiv or ref.'d journals.
    The subject is fascinating simply because black hole event horizons become complexified if they exceed `extreme' classification, and go over into naked singularities (NS).
    Since GR is limited to a real manifold, the problem of NS might become tractable in a complex version of GR...
    Any thoughts, references ?
     
  2. jcsd
  3. Sep 1, 2009 #2

    atyy

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    http://arxiv.org/abs/gr-qc/9312032
    Ashtekar Variables in Classical General Realtivity
    Domenico Giulini
    "Chapter three considers complex General Relativity and shows how its field equations can be obtained from a variational principle involving only the self dual part of the connection. In chapter four the (3+1)-decomposition is presented in as much detail as seemed necessary for an audience that does not consist entirely of canonical relativists. It is then applied to complex General Relativity in chapter five, where for the first time Ashtekar’s connection variables are introduced. The Hamiltonian of complex General Relativity is presented in terms of connection variables. In chapter six the constraints that follow from the variational principle are analyzed and their Poisson brackets are presented. In chapter seven we discuss the reality conditions that have to be imposed by hand to select real solutions, and briefly sketch the geometric interpretation of the new variables. In chapter 8 we indicate how the Hamiltonian has to be amended by surface integrals in the case of open initial data hypersurfaces with asymptotically flat data. It ends with a demonstration of the positivity of the mass at spatial infinity for maximal hypersurfaces."
     
  4. Sep 1, 2009 #3

    Jim

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    Very nice pedagogical intro to LQG, Atyy.
    However, I was not thinking of LQG, but just a generalization of the GR field eqs, via either a complex metric or connexion. In particular, I am interested in learning of such a formulation which is then applied to either Kerr or Kerr-Newman BHs, and whether in the extremal limits, such BHs morph into naked singularities. I suspect there is something terribly intractable about formulating GR on a complex (3+1) manifold, or many people other than Ashtekar would've attempted it by now, in an attempt to generalize GR.
     
  5. Sep 1, 2009 #4

    atyy

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