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Abstract: We explore the properties of test-particle orbits in -bumpy- spacetimes -stationary, reflection-symmetric, asymptotically flat solutions of Einsteinequations that have a non-Kerr anomalous higher-order multipole-momentstructure but can be tuned arbitrarily close to the Kerr metric. Futuredetectors should observe gravitational waves generated during inspirals ofcompact objects into supermassive central bodies. If the central body deviatesfrom the Kerr metric, this will manifest itself in the emitted waves. Here, weexplore some of the features of orbits in non-Kerr spacetimes that might leadto observable signatures. As a basis for this analysis, we use a family ofexact solutions proposed by Manko and Novikov which deviate from the Kerr metricin the quadrupole and higher moments, but we also compare our results to otherwork in the literature. We examine isolating integrals of the orbits and findthat the majority of geodesic orbits have an approximate fourth constant of themotion in addition to the energy, angular momentum and rest mass and theresulting orbits are tri-periodic to high precision. We also find that thisfourth integral can be lost for certain orbits in some oblately deformedManko-Novikov spacetimes. However, compact objects will probably not end up onthese chaotic orbits in nature. We compute the location of the innermost stablecircular orbit ISCO and find that the behavior of orbtis near the ISCO can bequalitatively different depending on whether the ISCO is determined by theonset of an instability in the radial or vertical direction. Finally, wecompute periapsis and orbital-plane precessions for nearly circular and nearlyequatorial orbits in both the strong and weak field, and discuss weak-fieldprecessions for eccentric equatorial orbits.

Author: Jonathan R Gair, Chao Li, Ilya Mandel

Source: https://arxiv.org/

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