Citation
Cohen, Michael Isaac (2011) Topics in gravitation  numerical simulations of event horizons and parameter estimation for LISA. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:08032010144145071
Abstract
In Part I, we consider numerical simulations of event horizons. Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to find event horizons in numerical spacetimes, and find that straightforward integration of geodesics backward in time is most robust. We apply this method to various systems, from a highly spinning Kerr hole through to an asymmetric binary black hole inspiral. We find that the exponential rate at which outgoing null geodesics diverge from the event horizon of a Kerr black hole is the surface gravity of the hole. In headon mergers we are able to track quasinormal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. In the headon “kick” merger, we find that computing the LandauLifshitz velocity of the event horizon is very useful for an improved understanding of the kick behaviour. Finally, in the inspiral simulations, we find that the topological structure of the black holes does not produce an intermediate toroidal phase, though the structure is consistent with a potential reslicing of the spacetime in order to introduce such a phase. We further discuss the topological structure of nonaxisymmetric collisions.
In Part II, we consider parameter estimation of cosmic string burst gravitational waves in Mock LISA data. A network of observable, macroscopic cosmic (super)strings may well have formed in the early Universe. If so, the cusps that generically develop on cosmicstring loops emit bursts of gravitational radiation that could be detectable by gravitationalwave interferometers, such as the groundbased LIGO/Virgo detectors and the planned, spacebased LISA detector. We develop two versions of a LISAoriented stringburst search pipeline within the context of the Mock LISA Data Challenges, which rely on the publicly available MultiNest and PyMC software packages, respectively. We use the Fstatistic to analytically maximize over the signal’s amplitude and polarization, A and psi, and use the FFT to search quickly over burst arrival times t_C. We also demonstrate an approximate, Bayesian version of the Fstatistic that incorporates realistic priors on A and psi. We calculate how accurately LISA can expect to measure the physical parameters of stringburst sources, and compare to results based on the Fishermatrix approximation. To understand LISA’s angular resolution for stringburst sources, we draw maps of the waveform fitting factor [maximized over (A,psi,t_C)] as a function of sky position; these maps dramatically illustrate why (for LISA) inferring the correct sky location of the emitting string loop will often be practically impossible. In addition, we identify and elucidate several symmetries that are embedded in this search problem, and we derive the distribution of cutoff frequencies f_max for observable bursts.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  event horizon numerical relativity binary black hole merger parameter estimation cosmic string LISA MLDC  
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:  26 July 2010  
Funders: 
 
Record Number:  CaltechTHESIS:08032010144145071  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:08032010144145071  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  5984  
Collection:  CaltechTHESIS  
Deposited By:  Michael Cohen  
Deposited On:  14 Sep 2010 21:15  
Last Modified:  26 Dec 2012 04:29 
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