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April 19, 20260 citationsOpen Access

Dark Energy as Rotational Kinetic Energy: A Geometric Origin for the Cosmological Constant

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RKRonald Kyle

Key Points

  • The aim is to explore the relationship between dark energy and rotational kinetic energy, providing a geometric origin for the cosmological constant.
  • Removed the Raychaudhuri equation to clarify arguments.
  • Utilized a lower-dimensional model to illustrate concepts.
  • Provided a crude animation demonstrating the geometrical ideas.
  • Demonstrated how rotation leads to a geometric understanding of time and space.
  • Provided a solid argument for interpreting dark energy in terms of rotational kinetic energy.

Abstract

Removed the Raychaudhuri equation, but the essence is the same. A rotating flat B4 is essentially an instanton at any given instant from observers inside Minkowski Physical spacetime. (3+1) (I propose we refer to Minkowski spacetime as (4D-1) and the instanton and kinematic space as 4D. Not in the paper though.) v0.997b (This version)- Major rework- the Raychaudhuri equation did not end up working out. I realized I was holding onto it for some reason and so now I have let it go and I feel the entire argument is much more solid overall. I may submit this version to a journal; still need to double check everything. v0.993b -Updated with some better wording and a few better arguments. I show how a lower-dimensional model (tennis ball and flatland appendix) demonstrates how time's hyperbolic orthogonality with space is achieved for a 2D+1D observer living on the surface of a 3D ball through simple rotation. There is a crude animation made in manim for python of the tennis ball example included as tennisball3d.mp4 WIP not yet final v0.997b

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Cite This Study

Ronald Kyle (2026) studied this question.

synapsesocial.com/papers/69e4741c010ef96374d8fe94https://doi.org/10.5281/zenodo.19622212
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