We rederive the equations of motion for relativistic strings, that is,one-dimensional elastic bodies whose internal energy depends only on theirstretching, and use them to study circular string loops rotating in theequatorial plane of flat and black hole spacetimes. We start by obtaining theconditions for equilibrium, and find that: (i) if the string's longitudinalspeed of sound does not exceed the speed of light then its radius when rotatingin Minkowski's spacetime is always larger than its radius when at rest; (ii) inMinkowski's spacetime, equilibria are linearly stable for rotation speeds belowa certain threshold, higher than the string's longitudinal speed of sound, andlinearly unstable for some rotation speeds above it; (iii) equilibria arealways linearly unstable in Schwarzschild's spacetime. Moreover, we studyinteractions of a rotating string loop with a Kerr black hole, namely in thecontext of the weak cosmic censorship conjecture and the Penrose process. Wefind that: (i) elastic string loops that satisfy the null energy conditioncannot overspin extremal black holes; (ii) elastic string loops that satisfythe dominant energy condition cannot increase the maximum efficiency of theusual particle Penrose process; (iii) if the dominant energy condition (but notthe weak energy condition) is violated then the efficiency can be increased.This last result hints at the interesting possibility that the dominant energycondition may underlie the well known upper bounds for the efficiencies ofenergy extraction processes (including, for example, superradiance).
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