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

• 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.