206,395 research outputs found

    Compact Binary Waveform Center-of-Mass Corrections

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    We present a detailed study of the center-of-mass (c.m.) motion seen in simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration. We investigate potential physical sources for the large c.m. motion in binary black hole simulations and find that a significant fraction of the c.m. motion cannot be explained physically, thus concluding that it is largely a gauge effect. These large c.m. displacements cause mode mixing in the gravitational waveform, most easily recognized as amplitude oscillations caused by the dominant (2,±\pm2) modes mixing into subdominant modes. This mixing does not diminish with increasing distance from the source; it is present even in asymptotic waveforms, regardless of the method of data extraction. We describe the current c.m.-correction method used by the SXS collaboration, which is based on counteracting the motion of the c.m. as measured by the trajectories of the apparent horizons in the simulations, and investigate potential methods to improve that correction to the waveform. We also present a complementary method for computing an optimal c.m. correction or evaluating any other c.m. transformation based solely on the asymptotic waveform data.Comment: 20 pages, 15 figure

    Time-dependent current density functional theory via time-dependent deformation functional theory: A constrained search formulation in the time domain

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    The logical structure and the basic theorems of time-dependent current density functional theory (TDCDFT) are analyzed and reconsidered from the point of view of recently proposed time-dependent deformation functional theory (TDDefFT). It is shown that the formalism of TDDefFT allows to avoid a traditional external potential-to-density/current mapping. Instead the theory is formulated in a form similar to the constrained search procedure in the ground state DFT. Within this formulation of TDCDFT all basic functionals appear from the solution of a constrained universal many-body problem in a comoving reference frame, which is equivalent to finding a conditional extremum of a certain universal action functional. As a result the physical origin of the universal functionals entering the theory, as well as their proper causal structure becomes obvious. In particular, this leaves no room for any doubt concerning predictive power of the theory.Comment: revtex4, 24 page

    From the self-force problem to the Radiation reaction formula

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    We review a recent theoretical progress in the so-called self-force problem of a general relativistic two-body system. Although a two-body system in Newtonian gravity is a very simple problem, some fundamental issues are involved in relativistic gravity. Besides, because of recent projects for gravitational wave detection, it comes to be possible to see those phenomena directly via gravitational waves, and the self-force problem becomes one of urgent and highly-motivated problems in general relativity. Roughly speaking, there are two approaches to investigate this problem; the so-called post-Newtonian approximation, and a black hole perturbation. In this paper, we review a theoretical progress in the self-force problem using a black hole perturbation. Although the self-force problem seems to be just a problem to calculate a self-force, we discuss that the real problem is to define a gauge invariant concept of a motion in a gauge dependent metric perturbation.Comment: a special issue for Classical and Quantum Gravity, a review article of Capra Ranch Meeting

    Duality and Four-Dimensional Black Holes

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    We consider the effects of abelian duality transformations on static, spherically-symmetric, asymptotically flat string spacetimes in four dimensions, where the dilaton, axion, metric, and gauge fields are allowed to be nonzero. Independent of the alpha' expansion, there is a six-parameter family of such configurations, labelled by the charges characterizing the asymptotic behaviour of the various fields: ie their mass, dilaton charge, axion charge, electric charge, magnetic charge, and Taub-NUT parameter. We show that duality, based on time-translation invariance, maps these solutions amongst themselves, with the effect of interchanging two pairs of these six labels, namely: (1) the mass and dilaton charge, and (2) the axion charge and the Taub-NUT parameter. We consider in detail the special case of the purely Schwarzschild black hole, for which the mass of the dual configuration vanishes to leading order in alpha'. Working to next-to-leading order in alpha' for the bosonic and heterotic strings, we find that duality takes a black hole of mass M to a (singular) solution having mass - 1/(alpha' M). Finally, we argue that two solutions which are related by duality based on a noncompact symmetry are {\it not} always physically equivalent.Comment: plain TeX, 37 pages, no figures. We have made some minor improvements in presentation and have included some additional reference

    Kinematic quantities of finite elastic and plastic deformation

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    Kinematic quantities for finite elastic and plastic deformations are defined via an approach that does not rely on auxiliary elements like reference frame and reference configuration, and that gives account of the inertial-noninertial aspects explicitly. These features are achieved by working on Galilean spacetime directly. The quantity expressing elastic deformations is introduced according to its expected role: to measure how different the current metric is from the relaxed/stressless metric. Further, the plastic kinematic quantity is the change rate of the stressless metric. The properties of both are analyzed, and their relationship to frequently used elastic and plastic kinematic quantities is discussed. One important result is that no objective elastic or plastic quantities can be defined from deformation gradient.Comment: v5: minor changes, one section moved to an Appendix, 26 pages, 2 figure
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