TY - JOUR
T1 - The cosmic censor forbids naked topology
AU - Galloway, G. J.
AU - Woolgar, E.
PY - 1997/1
Y1 - 1997/1
N2 - For any asymptotically flat spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two underlying assumptions concerning the causal structure: that no compact set can signal to arbitrarily small neighbourhoods of spatial infinity ('i0-avoidance'), and that no future incomplete null geodesic is visible from future null infinity. We show that these and the focusing condition together imply that the domain of outer communications is simply connected. Furthermore, we prove lemmas that have as a consequence that if a future incomplete null geodesic were visible from infinity, then, given our i0-avoidance assumption, it would also be visible from points of spacetime that can communicate with infinity, and so would signify a true naked singularity.
AB - For any asymptotically flat spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two underlying assumptions concerning the causal structure: that no compact set can signal to arbitrarily small neighbourhoods of spatial infinity ('i0-avoidance'), and that no future incomplete null geodesic is visible from future null infinity. We show that these and the focusing condition together imply that the domain of outer communications is simply connected. Furthermore, we prove lemmas that have as a consequence that if a future incomplete null geodesic were visible from infinity, then, given our i0-avoidance assumption, it would also be visible from points of spacetime that can communicate with infinity, and so would signify a true naked singularity.
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U2 - 10.1088/0264-9381/14/1/001
DO - 10.1088/0264-9381/14/1/001
M3 - Article
AN - SCOPUS:0040151744
VL - 14
SP - L1-L7
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
SN - 0264-9381
IS - 1
ER -