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Investigations of Black-Hole Spectra: Purely-Imaginary Modes and Kerr Ringdown Radiation

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abstract
When black holes are perturbed they give rise to characteristic waves that propagate outwards carrying information about the black hole. In the linear regime these waves are described in terms of quasinormal modes (QNM). Studying QNM is an important topic which may provide a connection to the quantum theory of gravity in addition to their astrophysical applications. Quasinormal modes correspond to complex frequencies where the real part represents oscillation and the imaginary part represents damping. We have developed a new code for calculating QNM with high precision and accuracy, which we applied to the Schwarzschild and Kerr geometries. The high accuracy of our calculations was a significant improvement over prior work, allowing us to compute QNM much closer to the negative imaginary axis (NIA) than it was possible before. The existence of QNM on the NIA has remained poorly understood, but our high accuracy studies have highlighted the importance of understanding their nature. In this work we show how the purely-imaginary modes can be calculated with the help of the theory of confluent Heun polynomials with the conclusion that all modes on the NIA correspond to polynomial solutions. We also show that certain types of these modes correspond to Kerr QNM. Finally, using our highly accurate QNM data we model the ringdown, a remnant black hole's decaying radiation. Ringdown occurs in the final stages of such violent astrophysical events as supernovae and black hole collisions. We use our model to analyse the ringdown waveforms from the publicly available binary black hole coalescence catalog maintained by the SXS collaboration. In our analysis we use a number of methods: Fourier transform, multi-mode nonlinear fitting and waveform overlap. Both our fitting and overlap approach allow inclusion of many modes in the ringdown model with the goal being to extract information about the nature of the astrophysical source of the ringdown signal.
subject
black holes
confluent Heun equation
general relativity
gravitational waves
quasinormal modes
ringdown
contributor
Zalutskiy, Maxim Pavlovich (author)
Cook, Gregory B. (committee chair)
John, David J. (committee member)
Anderson, Paul R. (committee member)
Carlson, Eric D. (committee member)
Holzwarth, Natalie A. W. (committee member)
date
2016-08-25T08:35:20Z (accessioned)
2016-08-25T08:35:20Z (available)
2016 (issued)
degree
Physics (discipline)
identifier
http://hdl.handle.net/10339/62634 (uri)
language
en (iso)
publisher
Wake Forest University
title
Investigations of Black-Hole Spectra: Purely-Imaginary Modes and Kerr Ringdown Radiation
type
Dissertation

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