Citation
Nichols, David A. (2012) Visualizing, approximating, and understanding blackhole binaries. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05152012231012129
Abstract
Numericalrelativity simulations of blackhole binaries and advancements in gravitationalwave detectors now make it possible to learn more about the collisions of compact astrophysical bodies. To be able to infer more about the dynamical behavior of these objects requires a fuller analysis of the connection between the dynamics of pairs of black holes and their emitted gravitational waves. The chapters of this thesis describe three approaches to learn more about the relationship between the dynamics of blackhole binaries and their gravitational waves: modeling momentum flow in binaries with the LandauLifshitz formalism, approximating binary dynamics near the time of merger with postNewtonian and blackholeperturbation theories, and visualizing spacetime curvature with tidal tendexes and framedrag vortexes.
In Chapters 24, my collaborators and I present a method to quantify the flow of momentum in blackhole binaries using the LandauLifshitz formalism. Chapter 2 reviews an intuitive version of the formalism in the firstpostNewtonian approximation that bears a strong resemblance to Maxwell’s theory of electromagnetism. Chapter 3 applies this approximation to relate the simultaneous bobbing motion of rotating black holes in the superkick configurationequalmass black holes with their spins antialigned and in the orbital planeto the flow of momentum in the spacetime, prior to the black holes’ merger. Chapter 4 then uses the LandauLifshitz formalism to explain the dynamics of a headon merger of spinning black holes, whose spins are antialigned and transverse to the infalling motion. Before they merge, the black holes move with a large, transverse, velocity, which we can explain using the postNewtonian approximation; as the holes merge and form a single black hole, we can use the LandauLifshitz formalism without any approximations to connect the slowing of the final black hole to its absorbing momentum density during the merger.
In Chapters 57, we discuss using analytical approximations, such as postNewtonian and blackholeperturbation theories, to gain further understanding into how gravitational waves are generated by blackhole binaries. Chapter 5 presents a way of combining postNewtonian and blackholeperturbation theorieswhich we call the hybrid methodfor headon mergers of black holes. It was able to produce gravitational waveforms and gravitational recoils that agreed well with comparable results from numericalrelativity simulations. Chapter 6 discusses a development of the hybrid model to include a radiationreaction force, which is better suited for studying inspiralling blackhole binaries. The gravitational waveform from the hybrid method for inspiralling mergers agreed qualitatively with that from numericalrelativity simulations; when applied to the superkick configuration, it gave a simplified picture of the formation of the large blackhole kick. Chapter 7 describes an approximate method of calculating the frequencies of the ringdown gravitational waveforms of rotating black holes (quasinormal modes). The method generalizes a geometric interpretation of blackhole quasinormal modes and explains a degeneracy in the spectrum of these modes.
In Chapters 811, we describe a new way of visualizing spacetime curvature using tools called tidal tendexes and framedrag vortexes. This relies upon a timespace split of spacetime, which allows one to break the vacuum Riemann curvature tensor into electric and magnetic parts (symmetric, tracefree tensors that have simple physical interpretations). The regions where the eigenvalues of these tensors are large form the tendexes and vortexes of a spacetime, and the integral curves of their eigenvectors are its tendex and vortex lines, for the electric and magnetic parts, respectively. Chapter 8 provides an overview of these visualization tools and presents initial results from numericalrelativity simulations. Chapter 9 uses topological properties of vortex and tendex lines to classify properties of gravitational waves far from a source. Chapter 10 describes the formalism in more detail, and discusses the vortexes and tendexes of multipolar spacetimes in linearized gravity about flat space. The chapter helps to explain how nearzone vortexes and tendexes become gravitational waves far from a weakly gravitating, timevarying source. Chapter 11 is a detailed investigation of the vortexes and tendexes of stationary and perturbed black holes. It develops insight into how perturbations of (strongly gravitating) black holes extend from near the horizon to become gravitational waves.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  black holes; gravitational waves; analytical relativity; numerical relativity  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Physics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  30 April 2012  
Record Number:  CaltechTHESIS:05152012231012129  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:05152012231012129  
Related URLs: 
 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  7032  
Collection:  CaltechTHESIS  
Deposited By:  David Nichols  
Deposited On:  17 May 2012 15:48  
Last Modified:  26 Dec 2012 04:42 
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