The Relativistic Elasticity of Rigid Bodies

The aim of this paper is twofold. First, we set up the theory of elastic matter sources within the framework of general relativity in a self-contained manner. The discussion is primarily based on the presentation of Carter and Quintana but also includes new methods and results as well as some modifications that in our opinion make the theory more modern and transparent. For instance, the equations of motion for the matter are shown to take a neat form when expressed in terms ...

An elementary account of special relativity for school-children.

A detailed re-examination of the seminal paper on special relativity, taking into account recent work on the physical interpretation of the space-time Lorentz transformation as well as the modern understanding of classical elecromagnetism as a certain limit of the fundamental underlying theory --quantum electrodynamics-- is presented. Many errors both of physical principle and of a mathematical nature are uncovered. The `relativity of simultaneity' and `length contraction' ef...

We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines is expansion-free (constant size) and shear-free (constant shape). This definition of a system is anticipated to yield simple, exact geometr...

The historical significance of the problem of relativistic rigid rotation is reviewed in light of recently published correspondence between Einstein and the mathematician Vladimir Varicak from the years 1909 to 1913.

A lengthy bibliography of books referring to special and/or general relativity is provided to give a background for discussions on the historical use of the concept of relativistic mass.

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 ...

Kirchhoff's kinetic analogy relates the deformation of an incompressible elastic rod to the classical dynamics of rigid body rotation. We extend the analogy to compressible filaments and find that the extension is similar to the introduction of relativistic effects into the dynamical system. The extended analogy reveals a surprising symmetry in the deformations of compressible elastica. In addition, we use known results for the buckling of compressible elastica to derive the ...

Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects seem more natural by connecting with more elementary aspects of physics, particularly the physics of waves.

In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an in...