LIGO Document T1400622-v2

Dynamics and Electromagnetic Wave Signatures of Magnetized Neutron Stars near Black Holes

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T - Technical notes
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We derive the dipole tensor for a magnetic dipole in a curved space-time, and expand \( J^\mu \) in vector harmonics assuming a spherically symmetric spacetime. We then consider the specific case of a stationary, precessing magnetic dipole in a Schwarzschild background. For this case, we set up the equations that the electromagnetic fields satisfy, and derive expressions for them on the horizon. We solve this system numerically.
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