**ABSTRACT**

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.

**References**

[1] ‘tHooft, G. Dimensional Reduction in Quantum Gravity, Utrecht Preprint THU-93/26,

gr-qc/9310026; Susskind, L. The World as a Hologram, hep-th/9409089; ‘tHooft, G.

The Holographic Principle,hep-th/0003004.

[2] Bousso, R. The Holographic Principle, hep-th/0203101.

[3] Flanagan, E. E., D. Marolf and R. M. Wald, Proof of Classical Versions of the Bousso

Entropy Bound and of the Generalized Second Law, Phys. Rev. D62, 084035.hepth/9908070.

[4] Verlinde, E. On the Origin of Gravity and the Laws of Newton, hep-th/1001.0785.

[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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