Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
The non-integrability of the Zipoy-Voorhees metric
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The low frequency gravitational wave detectors like eLISA/NGO will give us the opportunity to test whether the supermassive compact objects lying at the centers of galaxies are indeed Kerr black holes. A way to do such a test is to compare the gravitational wave signals with templates of perturbed black hole spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV) spacetime (known also as the $\gamma$ spacetime) can be included in the bumpy black hole family, because it can be considered as a perturbation of the Schwarzschild spacetime background. Several authors have suggested that the ZV metric corresponds to an integrable system. Contrary to this integrability conjecture, in the present article it is shown by numerical examples that in general ZV belongs to the family of non-integrable systems.
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External quadrupolar distortion imprints on orbital dynamics and accretion structure in thin disks around deformed compact objects, with the radiating region's outer edge tied to the radiation-to-gas pressure transition.
Deviations from γ=1 in the Zipoy-Voorhees metric shift the (z,w,v) classification of periodic orbits and induce phase shifts plus amplitude modulations in their gravitational-wave signals.
citing papers explorer
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The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes
Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
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Analytic thin disks and rings in a class of nonasymptotically flat static spacetimes
External quadrupolar distortion imprints on orbital dynamics and accretion structure in thin disks around deformed compact objects, with the radiating region's outer edge tied to the radiation-to-gas pressure transition.
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Periodic orbits and their gravitational wave radiations in $\gamma$-metric
Deviations from γ=1 in the Zipoy-Voorhees metric shift the (z,w,v) classification of periodic orbits and induce phase shifts plus amplitude modulations in their gravitational-wave signals.