Probing the Nature of Black Holes with Gravitational Waves

In this thesis, I present a number of studies intended to improve our understanding of black holes using gravitational waves. Although black holes are relatively well understood from a theory perspective, many questions remain about the nature of the black holes in our Universe. According to general relativity, astrophysical black holes are fully described by just their mass and spin. Yet, relying on electromagnetic-based observatories alone, we still know very little about the distribution of black hole masses or spins. Moreover, as merging black holes are invisible to these electromagnetic observatories, we cannot rely on them to provide us with information about the binary black hole merger rate or binary black hole formation channels. However, by observing gravitational wave signals from these inherently dark binaries, we will soon have some answers to these questions. Indeed, the Laser Interferometer Gravitational-Wave Observatory (LIGO) has already revealed a great deal of new information about binary black holes; giving us an early glimpse into their mass and spin distributions and placing the first constraints on the binary black hole merger rate. This thesis contributes to the goal of probing the nature of black holes with gravitational waves. Binary black holes can form as an isolated binary in the galactic field or through dynamical encounters in high-density environments. Dynamical formation can significantly alter the binary parameters, which then become imprinted on the gravitational waveform. By simulating varying black hole populations in high-density globular clusters, we identify a population of highly eccentric binary black hole mergers that are characteristic of dynamical formation. Although these systems would circularize by the time they are visible in LIGO's frequency band, the future Laser Interferometer Space Antenna (LISA) is capable of distinguishing this population of eccentric mergers from the circular mergers expected of isolated field-formed binaries. As these dynamically formed binaries depend on the size of the underlying black hole population in globular clusters, we can utilize the dynamically formed merger rate to infer globular cluster black hole populations -- allowing us to reveal information about binary black hole birth environments. In order to properly estimate the parameters of binary black holes from detected gravitational wave signals, such as their masses and spins, high-accuracy waveforms are a needed. The highest accuracy waveforms are those produced by numerical relativity simulations, which solve the full Einstein equations. Using the Spectral Einstein Code (SpEC), we expand the reach of numerical relativity to simulate binary black holes with nearly extremal spins, i.e., black holes with spins near the maximal value χ = 1. These waveforms are used to calibrate existing waveform approximants used in LIGO data analyses. This ensures that the systematic errors in these approximants are small enough that if highly-spinning systems are observed, the spins are recovered without bias. Although rapidly spinning binaries have remained elusive thus far, these waveforms ensure that the highest-spin systems can be detected in the quest to uncover the spin distribution of black holes. The end state of a binary black hole merger is a newly born, single black hole that rings down like a struck bell, sending its last few ripples of gravitational waves out into the spacetime. Embedded in this 'ringdown' signal are a multitude of specific frequencies. Einstein's theory of general relativity precisely predicts the ringdown frequencies of a black hole with a given mass and spin. The statement that a black hole is entirely described by just these two parameters is known as the no-hair theorem. For black holes that obey the laws of general relativity (and consequently, the no-hair theorem), these frequencies serve as a fingerprint for the black hole. However, if the objects we observe are not Einstein's black holes, but instead something more exotic, the frequencies will not have this property and this would be a spectacular surprise. A minimum of two tones are required for this test, each with an associated frequency and damping time that depend only on the mass and spin. The conventional no-hair test relies on the so-called 'fundamental' tones of a black hole. A test relying on the fundamental modes is not expected to be feasible for another ~10-15 years, after detector sensitivity has improved significantly. However, by analyzing the ringdown of high-accuracy numerical relativity waveforms, we show that modes beyond the fundamental, known as 'overtones', are detectable in current detectors. The overtones are short-lived, but this is countered by the fact that they can initially be much stronger than the fundamental mode. By measuring two tones in the ringdown of GW150914 we perform a first test of the no-hair theorem. While the current constraints are rather loose, this first test serves as a proof of principle. This is just one example of the powerful tests that can be employed with overtones using present day detectors and the even more precise tests that can be accomplished with LISA in the future.

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