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

The Mechanics of Spacetime – A Solid Mechanics Perspective on the Theory of General Relativity 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 of Hooke’s Law,
is analogous to that of spacetime per the Field Equations of General Relativity. We
relate properties of the fabric such as strain, stress, vibrations, and elastic moduli
to properties of gravity and space, such as gravitational potential, gravitational
acceleration, gravitational waves, and the density of vacuum. By introducing a
mechanical analogy of General Relativity, we enable the application of Solid Mechanics
tools to addressing problems in Cosmology.