Jackson Bates

Abstract

Numerical Relativity simulations play an important role in the Astrophysics community through their ability to create templates and test specific solutions to Einstein’s Field Equations. As Gravitational Wave Astronomy has grown over the past decades, the need for accurate and efficient codes has grown as well. Binary Black Hole Merger simulations provide the template needed by modern Gravitational Wave Detectors (LIGO/Virgo) to verify the integrity of detected symbols.

Improvement of these merger simulations aids both the experimental and numerical sides of physics, as well as verifying the theoretical side. A major issue that arises from any numerical simulation of a dynamical spacetime related to how one can uniquely determine the radiation content. Because gravitational radiation can only be determined uniquely infinitely far from the source, current simulations use various means to extrapolate an approximate waveform at finite r out to infinity. In this work, we extend upon existing tools to perform this extrapolation using Cauchy-Characteristic matching (CCE). CCE uses data from a Cauchy evolution of a spacetime with radiation to generate boundary data for a second evolution, this time using Characterisitic evolution techniques, to solve for the spacetime in the vicinity of future null infinity.

Here, we consider various ways of obtaining the necessary boundary data.

In particular, we are interested in finding new techniques that are more robust against various sources of high-frequency numerical noise. We compare these new techniques with the original CCE algorithm, as well as purely perturbative algorithms that extrapolate the waveform at finite r to infinity without the use of a second evolution step. Many of these newer methods perform just as accurately as their predecessor, while providing evidence towards increased efficiency in storage and computation time. Further investigation points toward the need to increase computational resolution in order to find more significant differences between these various methods. For our study, we considered the case of two equal-mass black holes at close separation merging into a final larger black hole. This case is well suited for standard perturbative extraction techniques, which allowed us to use the perturbative waveforms as an exact solution to compare to the CCE waveforms. We found that for the low-amplitude waveform modes, the numerical errors associated with poor resolution dominated the signals.

While we did see see some evidence that CCE produced a lower error than the perturbative extraction techniques, because the noise dominated both signals, we could not make strong conclusions about the efficacy of CCE.

In the end, we found that a new, much more efficient, algorithm for obtaining CCE data was at least as accurate as the older techniques (while being a factor of ∼5 faster). With this new technique, Cauchy codes can produce CCE initial data with minimal effects on the overall runtime.

Publication Date

8-15-2023

Document Type

Master's Project

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

Mathematical Sciences, School of

College

College of Science

Advisor

Yosef Zlochower

Advisor/Committee Member

Joshua Faber

Advisor/Committee Member

Nathaniel Barlow

Campus

RIT – Main Campus

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