Proposal
The Cosmic Fabric Model (CFM) (Tenev and Horstemeyer 2018a; Tenev 2018) considers the universe as a solid, elastic, thin ether existing in four spatial dimensions. Matter is postulated to prescribe volumetric strain on the fabric, and the lapse rate of time is postulated to dilate in the presence of strain (Tenev and Horstemeyer 2018a). By applying continuum mechanics to the fabric of space, Tenev and Horstemeyer (2018b) derived that the linearized action of the fabric is equivalent to the linearized Einstein-Hilbert Action, resulting in the Einstein Field Equations from a continuum mechanics standpoint. Further, the linearized Schwarzschild metric was also derived from the continuum mechanics of the fabric (Tenev and Horstemeyer 2019a). CFM then provided an elegant solution to the dark matter effect (Tenev and Horstemeyer 2019b; Tenev 2018) where additional gravitation is caused by the inherent structure of the fabric.
Using the simplifying assumption of near-static fields (low strain rates), Tenev and Horstemeyer (2018a) applied Hooke’s Law in the case of bending plates to decompose the total elastic energy of the fabric into the bending energy and membrane energy of the hypersurface. The membrane energy vanished, and the bending energy was shown to equate to the Lagrangian of the linearized Einstein-Hilbert Action.
We seek to lift the near-static field assumption and to generalize CFM to high strain rates. To demonstrate the high strain rate effect, we first note a key connection between the metric tensor and the strain tensor from continuum mechanics. This allows us to model time derivatives and four-dimensional shear terms. What looks like shear terms with the time axis is shown to be three-dimensional velocity-related terms. Applying only the assumption of small strains (the weak gravity regime), we obtain an equation that extends the behavior of the fabric to now include the case of high strain rates.
We then verify CFM’s compatibility with gravitational waves. This validates the analysis already completed by Tenev (2018; Tenev and Horstemeyer 2018a) who showed that the harmonic gauge condition is satisfied and that the linearized Ricci scalar can be employed. A wave equation for gravitational waves was derived, showing that the maximum shear wave speed is the speed of light. They demonstrated that the waves would exist with two degrees of freedom which corresponds to the polarization of gravitational waves.
Previously, the kinetic energy term of the Lagrangian was ignored, but it needs to be accounted for now that we consider high strain rates. However, in relativity, kinetic energy is relative to the observer and thus not Lorentz invariant. A relativistic formulation of the fabric’s Lagrangian is considered where the role of the “kinetic energy” is represented by a rest mass-energy term. A density for the fabric of space is considered and presently taken as a parameter of the model. We discuss how the physical meaning of this term is likely related to the Cosmological Constant. However, a formal interpretation of this term will require rigorous analysis that is outside of the scope of this research.
This analysis illustrates that CFM is a viable model in more general cases than was previously considered. Our analysis demonstrates the ability of the model to represent gravitational waves as mechanical propagation through the fabric at the speed of light. It also offers some hints to a mechanical understanding of the Cosmological Constant. The idea that human-relatable concepts, such as fabrics and engineering principles, can be leveraged to understand the universe is indicative that God designed and optimized the cosmos for comprehension. CFM is developed from the viewpoint that the universe was engineered by God, the ultimate Creationeer®, for mankind to behold the greatness of their Maker.
References
Tenev, T.G. 2018. An Elastic Constitutive Model of Spacetime and Its Applications [dissertation]. Starkville, Mississippi: Mississippi State University.
Tenev, T.G. and M.F. Horstemeyer. 2018a. Mechanics of spacetime — A solid mechanics perspective on the Theory of General Relativity. International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology 27, no. 1850083. DOI: 10.1142/S0218271818500839.
Tenev, T.G. and M.F. Horstemeyer. 2018b. Recovering the principle of relativity from the Cosmic Fabric Model of space. Reports in Advances of Physical Sciences 2, no. 1850011–13. DOI: 10.1142/S2424942418500111.
Tenev, T.G. and M.F. Horstemeyer. 2019a. The spacetime metric of a spherically symmetric deformation of space derived from the Cosmic Fabric Model of gravity. International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology 28, no. 1950096. DOI: 10.1142/S0218271819500962.
Tenev, T.G. and M.F. Horstemeyer. 2019b. Dark matter effect attributed to the inherent structure of cosmic space. International Journal of Modern Physics D, Gravitation, Astrophysics, Cosmology 28, no. 1950082. DOI: 10.1142/S0218271819500822.
Creationeer®and its derivatives are registered trademarks of Liberty University.
Keywords
gravitational waves, ether, Cosmic Fabric Model, relativity, high strain rates
Submission Type
Oral Presentation
Copyright
© 2025 Cameron Ward, Tichomir G. Tenev, and Mark Horstemeyer. All rights reserved.
Included in
Cosmology, Relativity, and Gravity Commons, Engineering Physics Commons, Mechanics of Materials Commons
Gravitational Waves as Vibrations on the Cosmic Fabric
The Cosmic Fabric Model (CFM) (Tenev and Horstemeyer 2018a; Tenev 2018) considers the universe as a solid, elastic, thin ether existing in four spatial dimensions. Matter is postulated to prescribe volumetric strain on the fabric, and the lapse rate of time is postulated to dilate in the presence of strain (Tenev and Horstemeyer 2018a). By applying continuum mechanics to the fabric of space, Tenev and Horstemeyer (2018b) derived that the linearized action of the fabric is equivalent to the linearized Einstein-Hilbert Action, resulting in the Einstein Field Equations from a continuum mechanics standpoint. Further, the linearized Schwarzschild metric was also derived from the continuum mechanics of the fabric (Tenev and Horstemeyer 2019a). CFM then provided an elegant solution to the dark matter effect (Tenev and Horstemeyer 2019b; Tenev 2018) where additional gravitation is caused by the inherent structure of the fabric.
Using the simplifying assumption of near-static fields (low strain rates), Tenev and Horstemeyer (2018a) applied Hooke’s Law in the case of bending plates to decompose the total elastic energy of the fabric into the bending energy and membrane energy of the hypersurface. The membrane energy vanished, and the bending energy was shown to equate to the Lagrangian of the linearized Einstein-Hilbert Action.
We seek to lift the near-static field assumption and to generalize CFM to high strain rates. To demonstrate the high strain rate effect, we first note a key connection between the metric tensor and the strain tensor from continuum mechanics. This allows us to model time derivatives and four-dimensional shear terms. What looks like shear terms with the time axis is shown to be three-dimensional velocity-related terms. Applying only the assumption of small strains (the weak gravity regime), we obtain an equation that extends the behavior of the fabric to now include the case of high strain rates.
We then verify CFM’s compatibility with gravitational waves. This validates the analysis already completed by Tenev (2018; Tenev and Horstemeyer 2018a) who showed that the harmonic gauge condition is satisfied and that the linearized Ricci scalar can be employed. A wave equation for gravitational waves was derived, showing that the maximum shear wave speed is the speed of light. They demonstrated that the waves would exist with two degrees of freedom which corresponds to the polarization of gravitational waves.
Previously, the kinetic energy term of the Lagrangian was ignored, but it needs to be accounted for now that we consider high strain rates. However, in relativity, kinetic energy is relative to the observer and thus not Lorentz invariant. A relativistic formulation of the fabric’s Lagrangian is considered where the role of the “kinetic energy” is represented by a rest mass-energy term. A density for the fabric of space is considered and presently taken as a parameter of the model. We discuss how the physical meaning of this term is likely related to the Cosmological Constant. However, a formal interpretation of this term will require rigorous analysis that is outside of the scope of this research.
This analysis illustrates that CFM is a viable model in more general cases than was previously considered. Our analysis demonstrates the ability of the model to represent gravitational waves as mechanical propagation through the fabric at the speed of light. It also offers some hints to a mechanical understanding of the Cosmological Constant. The idea that human-relatable concepts, such as fabrics and engineering principles, can be leveraged to understand the universe is indicative that God designed and optimized the cosmos for comprehension. CFM is developed from the viewpoint that the universe was engineered by God, the ultimate Creationeer®, for mankind to behold the greatness of their Maker.
References
Tenev, T.G. 2018. An Elastic Constitutive Model of Spacetime and Its Applications [dissertation]. Starkville, Mississippi: Mississippi State University.
Tenev, T.G. and M.F. Horstemeyer. 2018a. Mechanics of spacetime — A solid mechanics perspective on the Theory of General Relativity. International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology 27, no. 1850083. DOI: 10.1142/S0218271818500839.
Tenev, T.G. and M.F. Horstemeyer. 2018b. Recovering the principle of relativity from the Cosmic Fabric Model of space. Reports in Advances of Physical Sciences 2, no. 1850011–13. DOI: 10.1142/S2424942418500111.
Tenev, T.G. and M.F. Horstemeyer. 2019a. The spacetime metric of a spherically symmetric deformation of space derived from the Cosmic Fabric Model of gravity. International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology 28, no. 1950096. DOI: 10.1142/S0218271819500962.
Tenev, T.G. and M.F. Horstemeyer. 2019b. Dark matter effect attributed to the inherent structure of cosmic space. International Journal of Modern Physics D, Gravitation, Astrophysics, Cosmology 28, no. 1950082. DOI: 10.1142/S0218271819500822.
Creationeer®and its derivatives are registered trademarks of Liberty University.