## Abstract

We explore different gauge choices in the moving puncture formulation in order to improve the accuracy of a linear momentum measure evaluated on the horizon of the remnant black hole produced by the merger of a binary. In particular, motivated by the study of gauges in which the damping term in the shift m eta takes on a constant value, we design a gauge via a variable shift parameter m eta(r(t)). This parameter takes a low value asymptotically, 1/m, and then takes on a value of approximately 2 at the final hole horizon. This eta then follows the remnant black hole as it moves due to its net recoil velocity. We find that this choice keeps the accuracy of the binary evolution. Furthermore, if the asymptotic value of the parameter mis chosen about or below 1.0, it produces more accurate results for the recoil velocity than the corresponding evaluation of the radiated linear momentum at infinity, for typical numerical resolutions. Detailed studies of an unequal mass q = m1/m2 = 1/3 nonspinning binary are provided and then verified for other mass ratios (q = 1/2; 1/5) and spinning (q = 1) binary black hole mergers. We also use a position and black hole mass dependent damping term, eta[x1(t); x2(t);m1;m2], in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a 7:1 mass ratio, and then use 15:1 and 32:1 binaries for a convergence study. Finally, we apply our new gauge to a 64:1 binary and a 128:1 binary to well cover the comparable and small mass ratio regimes. Finally, we perform an analytic study of two nonspinning binary systems with q = 1 and q = 1/3 that use Brill-Lindquist initial data. These spacetimes are rotated into a frame that is transverse, with two of the five Weyl scalars vanishing, and quasi-Kinnersley. We derive and evaluate an index D that, when used in conjunction with the Baker-Campanelli Specialty index S, allows us to analyze and classify these spacetimes into Petrov types in the strong-field regime and between the black holes. Also included is an appendix to be utilized in conjunction with the RIT Catalog. It provides scripts for generation of fitting coefficients for analytic formulae developed in [1], [2], and [3] for specific subsets of the full 777 waveform RIT Catalog. Finally, we use these scripts to generate fitting coefficients for all non-precessing binaries in the catalog.

## Library of Congress Subject Headings

Black holes (Astronomy)--Mathematical models; Double stars--Mathematical models

## Publication Date

6-14-2021

## Document Type

Dissertation

## Student Type

Graduate

## Degree Name

Mathematical Modeling (Ph.D)

## Department, Program, or Center

School of Mathematical Sciences (COS)

## Advisor

Carlos O. Lousto

## Advisor/Committee Member

Hans-Peter Bischof

## Advisor/Committee Member

Yosef Zlochower

## Recommended Citation

Rosato, Nicole, "Improvements and Analysis of Challenging Numerical Simulations of Binary Black Holes" (2021). Thesis. Rochester Institute of Technology. Accessed from

https://repository.rit.edu/theses/10901

## Campus

RIT – Main Campus

## Plan Codes

MATHML-PHD