Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process

Abstract

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

32 pages, 6 figures; v2: minor improvements; v3: small changes, matches final published version; v4: typos in the references fixed; v5: missing exponent added to Eq. (88)

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• Gedanken Experiments to Destroy a Black Hole II: Kerr-Newman Black Holes Cannot be Over-Charged or Over-Spun
• Revised upper limit to energy extraction from a Kerr black hole
• Ultra-high-energy debris from the collisional Penrose process
• Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
• Static self-gravitating elastic bodies in Einstein gravity
• Stationary Rotating Strings as Relativistic Particle Mechanics
• Energy extraction from Kerr black holes by rigidly rotating strings
• Dynamics of Bianchi type I elastic spacetimes
• Spherically symmetric steady states of John elastic bodies in general relativity
• Relativistic elastodynamics
• Cylindrically symmetric static solutions of the Einstein field equations for elastic matter
• Stability and the equation of state for kinky vortons

Cited by in corpus (6)

• Weak cosmic censorship conjecture in Kerr black holes of modified gravity
• Gravitational Interactions of Finite Thickness Global Topological Defects with Black Holes
• Free-falling motion of an elastic rigid rod towards a Schwarzschild black hole
• Scanning the parameter space of collapsing rotating thin shells
• String loop vibration around Schwarzschild black hole
• Relativistic elastic membranes: rotating disks and Dyson spheres