A relativistic generalisation of rigid motions
J Llosa, A Molina, D Soler
TL;DR
This paper introduces radar-holonomic congruences as a less restrictive alternative to Born-rigid motions in relativity, providing differential equations, integrability conditions, and an example with specified rotation.
Contribution
It formulates radar-holonomic congruences via differential equations and demonstrates their existence with prescribed rotation, expanding the framework for relativistic rigid motion.
Findings
Defined radar-holonomic congruences as a weaker form of rigidity.
Derived integrability conditions for these congruences.
Constructed an example with a specified worldline and rotation.
Abstract
Radar-holonomic congruences of wordlines are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are studied. We finally obtain an example of a radar-holonomic congruence containing a given worldline with a given value of the rotation on this line.
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