MG15 - Talk detail |
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Participant |
Witzany, Vojtech | |||||||
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Institution |
ZARM - Am Falturm 2 - Bremen - Bremen - Germany | |||||||
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Session |
BN9 |
Accepted |
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Order |
Time |
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Talk |
Oral abstract |
Title |
Hamiltonians for spinning bodies in curved space-time | |||||
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Abstract |
The motion of a small body in curved space-time can be modeled by the evolution of a referential point inside the body and a set of multipole moments attached to it. However, supplementary conditions are needed to specify which point from the the whole volume of the body is chosen as a reference. In this talk, I will present Hamiltonians which reproduce the equations of motion for such bodies at pole-dipole order under various supplementary conditions. Additionally, I will discuss the question of canonical coordinates on the phase space of the problem for the purpose of symplectic integration, extensions to quadrupole order, and applications of the results to extreme-mass-ratio inspirals. |
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Pdf file |
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Session |
BH2 |
Accepted |
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Order |
Time |
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Talk |
Oral abstract |
Title |
Weak conservation law from hidden symmetry of spinning black holes | |||||
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Abstract |
The Kerr space–time possesses a 'hidden symmetry', which exhibits itself in an unexpected conserved quantity along geodesics known as the Carter constant. In this talk, I answer the question whether this hidden symmetry can be used to formulate a conservation law for a general matter field. First, I show that there cannot exist a conserved sum of Carter constants for a matter system with momentum exchange between its components. Then, I derive a 'weak' conservation law associated with the hidden symmetry and demonstrate its properties. Finally, I show how this weak conservation law and related identities can be used to detect violations of the evolution equations in numerical simulations of astrophysical processes near spinning black holes. |
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Pdf file |
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