3D Grazing Collision of Two Black Holes

Abstract

We present results for two colliding black holes (BHs), with angular momentum, spin, and unequal mass. For the first time, gravitational waveforms are computed for a grazing collision from a full 3D numerical evolution. The collision can be followed through the merger to form a single BH, and through part of the ringdown period of the final BH. The apparent horizon is tracked and studied, and physical parameters, such as the mass of the final BH, are computed. The total energy radiated in gravitational waves is shown to be consistent with the total initial mass of the spacetime and the apparent horizon mass of the final BH. DOI: 10.1103/PhysRevLett.87.271103 PACS numbers: 04.25.Dm, 04.30.Db, 95.30.Sf, 97.60.Lf The collision of two black holes (BHs) is considered by many researchers to be a primary candidate for generating detectable gravitational waves. As the first generation of gravitational wave detectors [1], with enough sensitivity to potentially detect waves, is coming online for the first time next year, the urgency of providing theoretical information needed not only to interpret, but also to detect the waves, is very high. However, even in axisymmetry, the problem has proven to be extremely difficult, requiring nearly 20 years to solve in even limited cases (e.g., [2 -5]). In full, 3D progress has been rather slow due to many factors, including (but not limited to) unexpected numerical instabilities, limited computer power, and the difficulties of dealing with spacetime singularities inside BHs. The first true 3D simulation of spinning and moving BHs was performed in [6]. In [6], the two BHs start out close to each other, much closer than the separation for the last stable orbit of a particle in the Schwarzschild spacetime, and the evolution proceeds through parts of the plunge and ring-down phase of a "grazing collision" within a very short time interval. The spacetime singularities are dealt with by a particular choice of coordinates, singularity avoiding slicing and vanishing shift. BH excision [7,8] has allowed improvements in the treatment of the spacetime singularities to the extent that highly accurate simulations of single BHs can be carried out [9][10][11][12] and recent applications to the grazing collision of BHs show promise [13]. One of the key limiting factors in the existing two approaches to the grazing collision is the achievable evolution time for which useful numerical data can be obtained, which due to numerical problems has been limited to 7M in [6], and to about 9M-15M in [13]. Here time is measured in units of the total Arnowitt-Deser-Misner (ADM) mass M of the system as opposed to using the bare mass m of one of the BHs.In this paper we consider singularity avoiding slicing as in [6]. We combine the application of a series of recently developed physics analysis tools and techniques with significant progress made in overcoming the problems mentioned above. Early, preliminary results from this series of simulations have been presented in [14,15], but we now provide the first de...

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