Browsing by Subject "Gravitational radiation"
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Item Boosted apparent horizons(2009-08) Akcay, Sarp; Matzner, Richard A. (Richard Alfred), 1942-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.Item Computing binary black hole merger waveforms using openGR(2012-05) McIvor, Greg Andrew; Matzner, Richard A. (Richard Alfred), 1942-; Gebhardt, Karl; Kumar, Pawan; Marder, Michael; Morrison, Philip; Press, WilliamOne of the most important predictions of General Relativity, Einstein’s theory of gravity, is the existence of gravitational radiation. The strongest source of such radiation is expected to come from the merging of black holes. Upgrades to large ground based interferometric detectors (LIGO, VIRGO, GEO 600) have increased their sensitivity to the point that the first direct observation of a gravitational wave is expected to occur within the next few years. The chance of detection is greatly improved by the use of simulated waveforms which can be used as templates for signal processing. Recent advances in numerical relativity have allowed for long stable evolution of black hole mergers and the generation of expected waveforms. openGR is a modular, open framework black hole evolution code developed at The University of Texas at Austin Center for Relativity. Based on the BSSN (strongly hyperbolic) formulation of Einstein’s equations and the moving puncture method, we are able to model the evolution of a binary black hole system through the merger and extract the gravitational radiation produced. Although we are generally interested in binary interactions, openGR is capable of handling any number of black holes. This work serves as an overview of the capabilities of openGR and a demonstration of the physics it can be used to explore.