Gyroscropes Orbiting Gargantuan Black Holes: Spinning Secondaries in Extreme Mass Ratio Inspirals
Large mass ratio binary black hole systems are essential for studying the two-body problem in general relativity and are key sources of low-frequency gravitational waves. These sources will be detectable by the Laser Interferometer Space Antenna (LISA), which is a planned space-based gravitational-w...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/156758 https://orcid.org/0000-0002-8435-9955 |
| Summary: | Large mass ratio binary black hole systems are essential for studying the two-body problem in general relativity and are key sources of low-frequency gravitational waves. These sources will be detectable by the Laser Interferometer Space Antenna (LISA), which is a planned space-based gravitational-wave observatory. At lowest order, the secondary body (smaller black hole) follows a geodesic of the more massive black hole's spacetime. Post-geodesic effects are needed to model the system accurately. Failure to incorporate these effects can introduce bias in tests of general relativity and compromise precision measurement of the larger black hole's properties. One very important post-geodesic effect is the gravitational self-force, which describes the small body's interaction with its own contribution to a binary's spacetime and includes the backreaction of gravitational-wave emission driving inspiral. Another post-geodesic effect, the spin-curvature force, is due to the smaller body's spin coupling to spacetime curvature. Exploiting the large mass-ratio approximation, this thesis presents a suite of mathematical and computational tools for precisely calculating bound orbits and inspiral of spinning bodies around rotating black holes.
In Chapters 3 and 4, we employ a frequency-domain formulation to describe completely general orbits of spinning bodies in curved spacetime. The small body's spin influences orbital frequencies and accumulated phases which are direct gravitational-wave observables. In Chapter 5, we combine the leading orbit-averaged backreaction of point-particle gravitational-wave emission with the spin-curvature force to construct the trajectory and associated gravitational waveform of a spinning body inspiraling into a Kerr black hole. To achieve this, we use a near-identity transformation (NIT) to rapidly compute trajectories for generic orbit and spin configurations. This efficiency is essential for the high-dimensional, long-duration waveforms of large mass-ratio binary systems. In Chapter 6, we describe how the framework of Chapters 3 and 4 can be used to generate gravitational wave fluxes for spinning bodies on completely generic orbits and discuss a ``shifted geodesic'' approximation scheme which could speed up the evaluation of these fluxes. This thesis introduces methods for accurately modeling completely general orbits of spinning bodies in large mass ratio binary black hole systems, enhancing gravitational-wave models for the LISA science program, and introducing a limit that can be computed precisely as a benchmark for calculations across all mass ratios. |
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