A Note on the Cylindrical Collapse of Counter-rotating Dust

One of the outstanding issues of general relativity is that of the final state of gravitational collapse. Understandably, much has been written about spherical collapse , but comparatively less is known about non-spherical geometries. Thorne’s seminal analysis of cylindrical collapse 2 led him to formulate the hoop conjecture, which essentially states that horizons form when and only when the gravitational mass of the system is confined within a maximum “circumference” in every direction . Subsequent numerical analyses of prolate and oblate collapse , and of gravitational radiation emission in aspherical collapse 5 were unable to refute Thorne’s conjecture. One of the best studied non-spherical cases is that of an infinite cylindrical shell of counter-rotating dust. A detailed analysis by Apostolatos and Thorne , using C-energy 7 balance arguments for sequences of momentarily static radiation free configurations, showed that collapse is halted by an infinitesimal amount of counter-rotation (and very likely, also by infinitesimally small net rotation); no horizons, nor curvature singularities form. A subsequent, more detailed analysis, of the non-rotating dust case, confirmed the non-occurrence of horizons .