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2016 | 30 | 26-44
Article title

On Holography and Statistical Geometrodynamics

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The Einstein theory of relativistic gravity encoded in the General Relativity Theory (GRT) is investigated from a holographic statistical geometrophysical viewpoint done so here for the first time. In so doing, the arguments are carried out systematically and the four laws of geometrodynamics are enunciated with a proper reasonable development. To do so, new objects characterizing the quantum geometry christened “geomets” are proposed to exist and it is also proposed that there exist geometrodynamic states that these geomets occupy. The geometrodynamic states are statistical states of different curvature and when occupied determine the geometry of the spacetime domain under scrutiny and thereby tell energy-momentum how to behave and distribute. This is a different take and the theory is developed further by developing the idea that the quantities appearing in the Einstein field equations are in fact physically realistic and measurable quantities called the geometrodynamic state functions. A complete covariant geometrodynamic potential theory is then developed thereafter. Finally a new quantity called the “collapse index” is defined and how the spacetime geometry curves is shown as a first order geometrodynamic phase transition using information bit saturation instead of the concept of temperature. Relationship between purely and only geometry and information is stressed throughout. . The statistical formula relating curvature and probability is inverted and interpretation is provided. This is followed by a key application in the form of a correspondence between the Euler-Poincaré formula and the proposed “extended Gibbs formula”. In an appendix the nub of the proof of the Maldacena conjecture is provided.
Physical description
  • Department of Mathematics, Gogte Institute of Technology, Udyambag, Belgaum (Belgavi) - 590 008, Karnataka, India
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  • [5] Caticha, A. Towards a Statistical Geometrodynamics, in Decoherence and Entropy in Complex Systems ed. By H.-T. Elze (Springer Verlag, 2004). gr-qc/0301061. ibid., The Information Geometry of Space and Time, gr-qc/0508108.
  • [6] Merali, Z. The Origins of Space and Time, Nature 500, 516, 29 Aug 2013.
  • [7] A. Sen, J. Math. Phys. 22(8) (1981) 1781; ibid., Int. J. Theor. Phys. 21 (1981) 1; ibid., Phys. Lett. 119B (1982) 89.
  • [8] A. Ashtekar, Phys. Rev. Lett. 57 (1986) 2244; ibid., Phys. Rev. D36 (1987) 1587.
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