Born rigidity, proposed by and later named after Max Born, is a concept in special relativity. It is one answer to the question of what, in special relativity, corresponds to the rigid body of non-relativistic classical mechanics.
The defining property of Born rigidity is locally constant distance in the co-moving frame for all points of the body in question. It is a very restrictive sense of rigidity; for example, the Ehrenfest paradox states that it is impossible to put a disk into rotation while maintaining its Born rigidity. Similarly, Bell's spaceship paradox demonstrates that if we have a body at rest and try to move it along its length, then its Born rigidity will be broken.
Several weaker substitutes have been proposed as rigidity conditions.
Note that Born rigidity is a constraint on the motion of an extended body, achieved by careful application of forces to different parts of the body. A body rigid in itself would violate special relativity, as its speed of sound would be infinite.
The Herglotz-Noether theorem states that it is impossible to impose a linear acceleration on a rotating Born-rigid object.
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