Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-09-04
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages, revtex4; slightly modified version of an essay submitted to the Gravity Research Foundation Competition; references u
Scientific paper
We show that four-dimensional Lorentzian metrics admitting a global spacelike Lie group of isometries, $G_{1}={\mathbb R}$, which obey the Einstein equations for vacuum and certain types of matter, cannot contain apparent horizons. The assumed global isometry allows for the dimensional reduction of the (3+1) system to a (2+1) picture, wherein the four-dimensional metric fields act formally as matter fields. A theorem by Ida allows one to check for the absence of apparent horizons in the dimensionally reduced spacetime, with the four-dimensional results following from the topological product nature of the corresponding manifold. We argue that the absence of apparent horizons in spacetimes with translational symmetry constitutes strong evidence for the validity of the hoop conjecture, and also hints at possible (albeit arguably unlikely) generic violations of strong cosmic censorship.
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