Diese Doktorarbeit behandelt neue Methoden der numerischen Evolution von Systemen mit binären Schwarzen Löchern. Wir analysieren und vergleichen Evolutionen von verschiedenen physikalisch motivierten Anfangsdaten und zeigen Resultate der ersten Evolution von so genannten 'Thin Sandwich' Daten, die von der Gruppe in Meudon entwickelt wurden. <br /> Zum ersten Mal wurden zwei verschiedene Anfangsdaten anhand von dreidimensionalen Evolutionen verglichen: die Puncture-Daten und die Thin-Sandwich Daten. Diese zwei Datentypen wurden im Hinblick auf die physikalischen Eigenschaften während der Evolution verglichen. <br /> Die Evolutionen zeigen, dass die Meudon Daten im Vergleich zu Puncture Daten wesentlich mehr Zeit benötigen bevor sie kollidieren. Dies deutet auf eine bessere Abschätzung der Parameter hin. Die Kollisionszeiten der numerischen Evolutionen sind konsistent mit unabhängigen Schätzungen basierend auf Post-Newtonschen Näherungen die vorhersagen, dass die Schwarzen Löcher ca. 60% eines Orbits rotieren bevor sie kollidieren. / This thesis presents new approaches to evolutions of binary black hole systems in numerical relativity. We analyze and compare evolutions from various physically motivated initial data sets, in particular presenting the first evolutions of Thin Sandwich data generated by the Meudon group. <br /> For the first time two different quasi-circular orbit initial data sequences are compared through fully 3d numerical evolutions: Puncture data and Thin Sandwich data (TSD) based on a helical killing vector ansatz. The two different sets are compared in terms of the physical quantities that can be measured from the numerical data, and in terms of their evolutionary behavior. <br /> The evolutions demonstrate that for the latter, "Meudon" datasets, the black holes do in fact orbit for a longer amount of time before they merge, in comparison with Puncture data from the same separation. This indicates they are potentially better estimates of quasi-circular orbit parameters. The merger times resulting from the numerical simulations are consistent with independent Post-Newtonian estimates that the final plunge phase of a black hole inspiral should take 60% of an orbit.

Boosted black holes play an important role in General Relativity (GR), especially in relation to the binary black hole problem. Solving Einstein vacuum equations in the strong field regime had long been the holy grail of numerical relativity until the significant breakthroughs made in 2005 and 2006. Numerical relativity plays a crucial role in gravitational wave detection by providing numerically generated gravitational waveforms that help search for actual signatures of gravitational radiation exciting laser interferometric detectors such as LIGO, VIRGO and GEO600 here on Earth. Binary black holes orbit each other in an ever tightening adiabatic inspiral caused by energy loss due to gravitational radiation emission. As the orbits shrinks, the holes speed up and eventually move at relativistic speeds in the vicinity of each other (separated by ~ 10M or so where 2M is the Schwarzschild radius). As such, one must abandon the Newtonian notion of a point mass on a circular orbit with tangential velocity and replace it with the concept of black holes, cloaked behind spheroidal event horizons that become distorted due to strong gravity, and further appear distorted because of Lorentz effects from the high orbital velocity. Apparent horizons (AHs) are 2-dimensional boundaries that are trapped surfaces. Conceptually, one can think of them as 'quasi-local' definitions for a black hole horizon. This will be explained in more detail in chapter 2. Apparent horizons are especially important in numerical relativity as they provide a computationally efficient way of describing and locating a black hole horizon. For a stationary spacetime, apparent horizons are 2-dimensional cross-sections of the event horizon, which is itself a 3-dimensional null surface in spacetime. Because an AH is a 2-dimensional cross-section of an event horizon, its area remains invariant under distortions due to Lorentz boosts although its shape changes. This fascinating property of the AH can be attributed to the fact that it is a cross-section of a null surface, which, under the boost, still remains null and the total area does not change. Although this invariance of the area is conceptually easy to see it is less straightforward to derive this result. We present two different ways to show the area invariance. One is based on the spin-boost transformation of the null tetrad and the other a direct coordinate transformation of the boosted metric under the Lorentz boost. Despite yielding identical results the two methods differ significantly and we elaborate on this in much more detail. We furthermore show that the use of the spin-boost transformation is not well-suited for binary black hole spacetime and that the spin-boost is fundamentally different from a Lorentz boost although the transformation equations look very similar. We also provide a way to visualize the distorted horizons and look at the multi-pole moments of these surfaces under small boosts. We finish by summarizing our main results at the end and by commenting on the binding energy of the binary and how the apparent horizon is distorted due to presence of another black hole. / text

Compact binary coalescing systems: binary neutron stars, neutron star black hole pairs and binary black hole systems, represent promising candidates for gravitational wave first detection and have the potential to provide precise tests of the strong-field predictions of general relativity. Observations of binary black hole (BBH) systems will provide a wealth of information relevant to fundamental physics, astrophysics and cosmology. The search for such systems is a major priority of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo collaborations. A major area of research within LIGO-Virgo analysis groups is incorporation of spin into the search template banks used for binary black hole systems. In this dissertation, I compare the injection efficiency and parameter recovery from three binary black hole searches. One of the searches presented here uses non-spinning templates and represents the standard LIGO search for binary black holes with total masses between 35 and 100M[circle with dot]. The other two use spin aligned and anti-aligned templates representing a future search for black hole binary systems with total masses between 35-100M[circle with dot]. One of the two spinning searches has the spin parameter set to zero, nonspinning, as a check of the spinning method. (Additionally the (anti-)aligned spin searches use a retooling of the standard pipeline taking advantage of a code base designed specifically to handle Advanced LIGO data.) All three searches were run on artificial data created by the Numerical Injection Analysis 2 collaboration (NINJA2) containing Gaussian noise and numerically generated signals modeling aligned and anti-aligned spinning binary black holes. I found that for the analyzed two weeks of data the three searches recover injections with nearly equal efficiency; however, the spinning search recovers the parameters of the injections more accurately than the non-spinning search. Specifically, the parameter recovery of the spins shows a correlation between the injected and recovered spins, and the addition of spin to the template bank improves the recovery of the signal-to-noise ratio and the chirp mass for an injected signal. While spin aligned situations are geometrically low probability configurations, there are plausible astrophysical effects that lead to alignment of spins prior to merger. Therefore my results show that the spin-aligned template bank search represents an improvement on the standard non-spinning search in the highmass region and should be pursued on real data. / text

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20903号 / 理博第4355号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々木 節, 教授 柴田 大, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM