TY - JOUR
T1 - Chaos in static axisymmetric spacetimes
T2 - I. Vacuum case
AU - Sota, Yasuhide
AU - Suzuki, Shingo
AU - Maeda, Kei Ichi
PY - 1996
Y1 - 1996
N2 - We study the motion of a test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (i) a local instability measured by the Weyl curvature, and (ii) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyse several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behaviour in some spacetimes, these can be accounted for by the second criterion.
AB - We study the motion of a test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (i) a local instability measured by the Weyl curvature, and (ii) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyse several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behaviour in some spacetimes, these can be accounted for by the second criterion.
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U2 - 10.1088/0264-9381/13/5/034
DO - 10.1088/0264-9381/13/5/034
M3 - Article
AN - SCOPUS:21344473884
SN - 0264-9381
VL - 13
SP - 1241
EP - 1260
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 5
ER -