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Unpolarized radiative cylindrical spacetimes: Trapped surfaces and quasilocal energy

Sergio M. C. V. Goncalves
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Abstract

We consider the most general vacuum cylindrical spacetimes, which are defined by two global, spacelike, commuting, non-hypersurface-orthogonal Killing vector fields. The cylindrical waves in such spacetimes contain both + and $\times$ polarizations, and are thus said to be unpolarized. We show that there are no trapped cylinders in the spacetime, and present a formal derivation of Thorne's C-energy, based on a Hamiltonian reduction approach. Using the Brown-York quasilocal energy prescription, we compute the actual physical energy (per unit Killing length) of the system, which corresponds to the value of the Hamiltonian that generates unit proper-time translations orthogonal to a given fixed spatial boundary. The C-energy turns out to be a monotonic non-polynomial function of the Brown-York quasilocal energy. Finally, we show that the Brown-York energy at spatial infinity is related to an asymptotic deficit angle in exactly the same manner as the specific mass of a straight cosmic string is to the former.

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Sergio M. C. V. Goncalves. 2002-12-30. Unpolarized radiative cylindrical spacetimes: Trapped surfaces and quasilocal energy. https://doi.org/10.1088/0264-9381%2F20%2F1%2F303

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