Motion preserving local proper distances measured on instantaneous comoving simultaneity slices. It constrains the acceleration of different points of a body, rather than describing an infinitely fast material signal. For rectilinear positive acceleration, the front of an extended Born-rigid body accelerates less strongly than its rear.
A front worldline at fixed proper distance along a rear observer's simultaneity slice is parametrized by the displayed equations, with velocity and Lorentz factor evaluated at the rear event. The front time is locally future-oriented when , where is the rear signed proper acceleration. At a zero of that factor the rigid coordinate extension encounters an acceleration-horizon obstruction.
Two rockets maintaining fixed separation in an inertial laboratory frame do not preserve their comoving separation. A string connecting them is stretched rather than remaining unstrained; sufficiently large strain can break a real string. The contrast with Born rigidity follows from relativity of simultaneity and does not contradict Lorentz contraction.
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Born rigidity is a concept in the field of relativistic physics, particularly in the context of special relativity. It refers to the idea of an object's ability to maintain its shape and size while moving through spacetime without undergoing any deformation due to relativistic effects. The term comes from the work of Hermann Minkowski and is named after Max Born, who contributed significantly to the understanding of the topic.