Abstract
We extend the Ori and Thorne (OT) procedure to compute the transition from an adiabatic inspiral into a geodesic plunge for any spin, with emphasis on near-extremal ones. Our analysis revisits the validity of the approximations made in OT. In particular, we discuss possible effects coming from eccentricity and nongeodesic past-history of the orbital evolution. We find three different scaling regimes according to whether the mass ratio is much smaller, of the same order or much larger than the near extremal parameter describing how fast the primary black hole rotates. Eccentricity and nongeodesic past-history corrections are always subleading, indicating that the quasicircular approximation applies throughout the transition regime. However, we show that the OT assumption that the energy and angular momentum evolve linearly with proper time must be modified in the near-extremal regime. Using our transition equations, we describe an algorithm to compute the full worldline in proper time for an extreme mass ratio inspiral (EMRI) and the resultant gravitational waveform in the high spin limit.
Highlights
The LIGO observation of the transient gravitational wave (GW) signal from the collision of two stellar mass black holes [1] in September 2015 spectacularly opened the new field of gravitational wave astronomy
We extend the Ori and Thorne (OT) procedure to compute the transition from an adiabatic inspiral into a geodesic plunge for any spin, with emphasis on near-extremal ones
We describe an algorithm to compute the full worldline in proper time for an extreme mass ratio inspiral (EMRI) and the resultant gravitational waveform in the high spin limit
Summary
The LIGO observation of the transient gravitational wave (GW) signal from the collision of two stellar mass black holes [1] in September 2015 spectacularly opened the new field of gravitational wave astronomy. The existence of a double pole in the function determining the black hole horizons in this limit is responsible for an enhancement of symmetry in the near horizon geometry of the Kerr black hole [15], a feature that remains true for any extremal black hole [16] This enhancement of symmetry from time translations to the conformal group has allowed several groups to analytically solve the master Teukolsky equation in the presence of the in spiraling probe particle leading to an analytic expression for the energy fluxes carried by the gravitational waves generated by this source [17,18,19,20,21,22,23,24,25].
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