Topics in Gravitation – Numerical Simulations of Event Horizons and Parameter Estimation for LISA

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 head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 105. In the head-on merger, we find that computing the Landau-Lifshitz 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 re-slicing of the spacetime in order to introduce such a phase. We further discuss the topological structure of non-axisymmetric 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 cosmic-string loops emit bursts of gravitational radiation that could be detectable by gravitational-wave interferometers, such as the ground-based LIGO/Virgo detectors and the planned, space-based LISA detector. We develop two versions of a LISA-oriented string-burst 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 F-statistic to analytically maximize over the signal’s amplitude and polarization, A and ψ, and use the FFT to search quickly over burst arrival times tC. We also demonstrate an approximate, Bayesian version of the F-statistic that incorporates realistic priors on A and ψ. We calculate how accurately LISA can expect to measure the physical parameters of string-burst sources, and compare to results based on the Fisher-matrix approximation. To understand LISA’s angular resolution for string-burst sources, we draw maps of the waveform fitting factor [maximized over (A, ψ, tC)] 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 cut-off frequencies fmax for observable bursts.