The Relativistic Elasticity of Rigid Bodies

We present a new approach to the theory of static deformations of elastic test bodies in general relativity based on a generalization of the concept of frame of reference which we identify with the concept of quo-harmonic congruence. We argue on the basis of this new approach that weak gravitational plane waves do not couple to elastic bodies and therefore the latter, whatever their shape, are not suitable antennas to detect them.

The manual contains (in Russian) solutions of 230 problems that were used by the author for a number of years at the tutorial seminars in the first year undergraduate course in Mechanics and special relativity at Novosibirsk State University. The manual consists of 36 chapters - according to the number of seminars in this course. In each chapter, from 5 to 10 problems are dealt with. Where possible, several solutions of the same problem are given in order the students to beco...

A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of its applicability.

We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations without symmetries.

It has been more than a century since first Lorentz and later Einstein explored relativistic events and still important consequences of that remains unclear to everybody. The present study extensively focus on Lorentz (Length) contraction phenomenon and takes a different approaches to explain how the shrinking of the body appears if exists. We utilized two postulates of Special Relativity that emphasizes constancy of speed of light and same physical laws in any inertial frame...

In this survey we review the progress made in the last ten years in understanding the Black Hole Rigidity problem in the setting of smooth spacetimes. We review both local and global results and discuss the main mathematical ideas behind them.

In this work we discuss different interpretations of mass in the relativistic dynamics. A new way to introduce mass is proposed. Our way is based on the relativistic equation of motion expressed in the form of the Newton$'$s second law. In this approach mass appears as a tensor, not as a scalar. The tensor mass allows us simply to describe anisotropic character of inert features of a relativistic object.

In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not equivalent. It is also shown that so called M\"oller rigid non-inertial frames are locally rigid, but do not exhibit global rigidity. The physical meaning of this phenomenon is discussed, as well as its relation to the non-Euclidean nature of sp...

This paper has been withdrawn by the author.

This paper deals with four topics: The first subject is Abraham's spherical electron, Lorentz's contracted electron and B\"ucherer's electron. The second topic is Einstein's 1905 relativity theory of the motion of an electron. Einstein obtained expressions for the longitudinal and transverse masses of the electron using the principle of relativity and that of the constancy of the velocity of light. The third topic is Einstein's reply to Ehrenfest's query. Einstein's above sol...