Asymptotics with Numerical Relativity: Gravitational Memory, BMS Frames, and Nonlinearities

Author: Mitman, Keefe Edward Alden

Year: 2024

Degree: Dissertation (Ph.D.)

Advisor: Teukolsky, Saul A.

Committee Members: Chatziioannou, Katerina; Teukolsky, Saul A.; Scheel, Mark; Weinstein, Alan Jay; Chen, Yanbei

Option: Physics

DOI: 10.7907/7akc-yg91

Abstract

With the recent commencement of the LIGO-Virgo-KAGRA (LVK) Collaboration's fourth observing run, the field of gravitational-wave physics is uniquely poised to collect even more accurate data from compact binary coalescences. Consequently, we will soon be able to perform more stringent tests of general relativity (GR). Because GR must, in some regime, be violated---either because the Universe is described by an alternative theory or because of the emergence of quantum effects---these tests of GR are crucial for unveiling new physics. Performing such tests, however, requires that our understanding of GR and gravitational waves is reliable. And, while there are many tools for unraveling Einstein's equations, the only one that is robust in every regime of GR is numerical relativity (NR): a means for computing accurate solutions to Einstein's equations with supercomputers.

In this thesis, I highlight some recent and impactful advancements that have been incorporated into NR simulations of binary black holes. In particular, I show how a more robust procedure for calculating the radiative data at future null infinity from NR simulations, called Cauchy-characteristic evolution (CCE), produces waveforms that exhibit a not-yet observed prediction of GR colloquially referred to as memory. This phenomenon corresponds to the permanent net displacement that two observers will experience due to the passage of transient gravitational radiation. Memory is of particular interest in the testing GR and theory communities because of its relation to asymptotic symmetries and scattering amplitude calculations in particle physics. With these contemporary CCE waveforms, I provide explicit methods to calculate the various memory effects and I also comment on their relative magnitudes and detectability in the near future. Apart from this, I also demonstrate the importance of controlling the BMS freedoms of these waveforms, i.e., their frame freedom at future null infinity, for building waveform models as well as for extracting physics, such as GR's nonlinearities, from the ringdown phase of binary black hole mergers.

As we start to enter the next phase of high-precision gravitational-wave astronomy, correctly modeling gravitational waves with NR simulations will play a crucial role in pushing Einstein's theory of relativity to its limits. It is the aim of this thesis to illustrate the importance of combining gravitational-wave theory and NR to not only improve our understanding of black holes and gravitational waves, but also further our prospects for unveiling the true nature of gravity within our universe.

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