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).

Scanning the parameter space of collapsing rotating thin shells

“…One can also assess the energy conditions as derived from a stress-energy tensor on the full spacetime, but being localized on the timelike hypersurface of the shell. The two descriptions are related: the weak energy condition on the shell is equivalent to the null energy condition on the full spacetime[30].J V Rocha and R Santarelli…”

Gravitational interactions of finite thickness global topological defects with black holes

“…The evolution of topological defects and especially strings in curved backgrounds has been investigated [81][82][83][84][85][86][87][88][89][90][91][92] under the thin defect approximation where the defects are assumed to have zero thickness and thus propagate via simplified forms of the action. For example the action that describes the evolution of a zero thickness string is the Nambu-Goto action which is proportional to the area of the world-sheet of the string.…”