The Mechanics of Spacetime - A Solid Mechanics Perspective on the Theory of General Relativity

Abstract

We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the "cosmic fabric" and spacetime with the fabric's world volume. Using a Lagrangian formulation, we show that the fabric's behavior as derived from Hooke's Law is analogous to that of spacetime per the Field Equations of General Relativity. The study is conducted in the limit of small strains, or analogously, in the limit of weak and nearly static gravitational fields. The Fabric's Lagrangian outside of inclusions is shown to have the same form as the Einstein-Hilbert Lagrangian for free space. Properties of the fabric such as strain, stress, vibrations, and elastic moduli are related to properties of gravity and space, such as the gravitational potential, gravitational acceleration, gravitational waves, and the energy density of free space. By introducing a mechanical analogy of General Relativity, we enable the application of Solid Mechanics tools to address problems in Cosmology.

References in corpus (4)

• Elastic theory of unconstrained non-Euclidean plates
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory
• On galaxy rotation curves from a continuum mechanics approach to modified gravity

Cited by in corpus (10)

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• Non-linear Plane Gravitational Waves as Space-time Defects
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• A robophysical model of spacetime dynamics
• Some geometrical aspects of gravitational waves using continuum mechanics analogy: State of the art and potential consequences
• Analogy of space-time as an elastic medium, estimation creep coefficient of space from MOND theory, gravitational lensing and via time data from the GPS effect, discussion of the results for dark matter and Einstein's field equation
• Dark matter effect attributed to the inherent structure of cosmic space
• Recovering the Principle of Relativity from the Cosmic Fabric Model of Space
• Analogy of space-time as an elastic medium -- Study of the perturbation tensor of the metric $h_{\mu \nu }$ through the prism of the analogy of the theory of elasticity -- Analysis and potential consequences
• A Cosmological Bragg Law: Interpreting the CMB as a Diffractogram of Foliated Spacetime