The Relativistic Elasticity of Rigid Bodies

The concept of velocity dependent mass, relativistic mass, is examined and is found to be inconsistent with the geometrical formulation of special relativity. This is not a novel result; however, many continue to use this concept and some have even attempted to establish it as the basis for special relativity. It is argued that the oft-held view that formulations of relativity with and without relativistic mass are equivalent is incorrect. Left as a heuristic device a prelimi...

Contents. 1. Introduction. 2. Kinematics of a Material Medium: Material Representation. 3. Kinematics of a Material Medium: Convected Differentials. 4. Kinematics of a Perfect Elastic Medium. 5. Small Gravitational Perturbations of an Elastic Medium.

We present and modernize Souriau's 1958 geometric framework for Relativistic continuous media, and enlighten the necessary and the ad hoc modeling choices made since, focusing as much as possible on the Continuum Mechanics point of view. We describe the general covariant formulation of Hyperelasticity in General Relativity, and then in the particular case of a static spacetime. Finally, we apply this formalism for the Schwarzschild's metric, and recover the Classical Galilean...

We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material invariance is established and shown to be a true covariance principle, unlike the Lorentz covariance, which is valid only for non-deforming frames in rectilinear relative motion. Thus, this paper establishes that electrodynamics can be ful...

This article is a partly pedagogical, partly historical and partly technical review of special relativity and its experimental foundations, in honor of the centenary of Einstein's annus mirabilis.

A critical look at the history of relativistic dynamics.

The traditional Fourier equation just allows us to study the evolution of temperature in an "undeformable" bar. The search for its relativistic variant is a task which is expected to fail because in relativity there are no undeformable bars. Rigid bodies, in the sense of "as rigid as possible", are deformables. In this work we show how to write in relativity the system of equations necessary to study simultaneously deformation and temperature evolution along a rigid deformabl...

A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are otherwise different in general relativity. Realizing the potentially great impact of the discovered corrections, an overview of the situation is provided resulting from the newly discovered crisis, amid the evidences defending the theory...

An experimental formula, sometimes named as Newton-collision-formula, (v1-v2) = - e.(u1-u2) relating relative-velocities before & after impact of two bodies under linear-collision, is commonly used successfully for study of collision-dynamics. Although it seems possible as shown in text-books [1,2] to derive this relation, assuming (defining) e as ratio of impulses during restitution & deformation; but as yet, neither a good theoretical-basis nor a general-derivation of this ...

We provide a faithful translation of Hans Richter's important 1948 paper "Das isotrope Elastizit\"atsgesetz" from its original German version into English. Our introduction summarizes Richter's achievements.