From Information Geometry to Information Gravity, Information Geometry as the Origin of Einstein’s Gravity: Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE)

John Onimisi Obidi

doi:10.13140/rg.2.2.14211.26405

January 1, 2026Open Access

From Information Geometry to Information Gravity, Information Geometry as the Origin of Einstein’s Gravity: Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE)

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Key Points

This research aims to establish the connection between Information Geometry and Einstein's theory of gravity through the Obidi action.
Analyzed the Obidi action and its transformations within the framework of Information Geometry.
Compared it with the Einstein–Hilbert action to derive implications for gravitational theory.
Utilized various metrics and entropic formulations to support the findings.
Established a defining correspondence between the Obidi action and the Einstein–Hilbert action.
Demonstrated that the results support the concept of Information Gravity as an emergent phenomenon.
Provided metrics and equations consistent with entropic principles and general relativity.

Implication

Demonstrates a correspondence between the Obidi action and Einstein–Hilbert action, indicating insights into gravity theory.

Abstract

Keywords: Theory of Entropicity (ToE); Obidi Action; Obidi Transformation; Obidi Metric; Obidi Relativistic Reduction Theorem; Einstein–Hilbert Action; Information Gravity; Information Geometry; Fisher–Rao metric; Fubini–Study metric; Bures metric; Amari–Čencov α-connections; Rényi–Tsallis entropy; Master Entropic Equation; Vuli–Ndlela Integral; Emergent Gravity; Entropic Field; General Relativity; Levi–Civita connection; Hybrid Metric-Affine Space (HMAS); Entropic Cosmological Constant.

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Cite This Study

John Onimisi Obidi (2026) studied this question.

synapsesocial.com/papers/6a21151ad499ed480b16e555 https://doi.org/10.13140/rg.2.2.14211.26405

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From Information Geometry to Information Gravity, Information Geometry as the Origin of Einstein’s Gravity: Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE)

Key Points

Implication

Abstract

Discussion

Cite This Study

From Information Geometry to Information Gravity, Information Geometry as the Origin of Einstein’s Gravity: Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE)

Key Points

Implication

Abstract

Discussion

Cite This Study

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