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We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the / = 2, m -- ±2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the superkick configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal-mode frequencies. We argue that this locking begins during the merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during the merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations. [ABSTRACT FROM AUTHOR]

We formulate a spherical harmonically decomposed 1 + 1 scheme to self-consistently evolve the trajectory of a point particle and its gravitational metric perturbation to a Schwarzschild background spacetime. Following the work of Moncrief, we write down an action for perturbations in spacetime geometry, combine that with the action for a point particle moving through this spacetime, and then obtain Hamiltonian equations of motion for metric perturbations, the particle's coordinates, as well as its canonical momenta. Hamiltonian equations for the metric perturbation and their conjugate momenta, for even and odd parities, reduce to Zerilli-Moncrief and Regge-Wheeler master equations with source terms, which are gauge invariant, plus auxiliary equations that specify the gauge. Hamiltonian equations for the particle, on the other hand, now include effect of metric perturbations--with these new terms derived from the same interaction Hamiltonian that lead to those well-known source terms. In this way, spacetime geometry and particle motion can be evolved in a self-consistent manner, in principle in any gauge. However, the point-particle nature of our source requires regularization, and we outline how the Detweiler-Whiting approach can be applied. In this approach, a singular field can be obtained analytically using the Hadamard decomposition of the Green's function and the regular field, which needs to be evolved numerically, is the result of subtracting the singular field from the total metric perturbation. In principle, any gauge that has the singular-regular field decomposition is suitable for our self-consistent scheme. In reality, however, this freedom is only possible if our singular field has a high enough level of smoothness. For a singular field with a minimum quality, one can adopt the Lorenz gauge condition, which we have recast into our formalism: for each l and m, we have two wave equations to evolve odd and even parity gauge invariant quantities and eigh first-order differential equations to fix the Lorenz gauge and determine the metric components. [ABSTRACT FROM AUTHOR]

We propose a modified configuration of an advanced gravitational-wave detector that is a speed-meter-type interferometer with improved sensitivity with respect to quantum noise. With the addition of polarization-controlling components to the output of an arm cavity Michelson interferometer, an orthogonal polarization state of the interferometer can be used to store signal, returning it later with opposite phase to cancel position information below the storage bandwidth of the opposite mode. This modification provides an alternative to an external kilometer-scale Fabry-Pérot cavity, as presented in earlier work of Purdue and Chen [Phys. Rev. D 66, 122004 (2002)]. The new configuration requires significantly less physical infrastructure to achieve speed meter operation. The quantity of length and alignment degrees of freedom is also reduced. We present theoretical calculations to show that such a speed meter detector is capable of beating the strain sensitivity imposed by the standard quantum limit over a broad range of frequencies for Advanced Laser Interferometer Gravitational-wave Observatory-like parameters. The benefits and possible difficulties of implementing such a scheme are outlined. We also present results for tuning of the speed meter by adjusting the degree of polarization coupling, a novel possibility that does not exist in previously proposed designs, showing that there is a smooth transition from speed meter operation to that of a signal-recycling Michelson behavior [ABSTRACT FROM AUTHOR]

Direct detection of gravitational radiation in the audio band is being pursued with a network of kilometer-scale interferometers (LIGO, Virgo, KAGRA). Several space missions (LISA, DECIGO, BBO) have been proposed to search for sub-hertz radiation from massive astrophysical sources. Here we examine the potential sensitivity of three ground-based detector concepts aimed at radiation in the 0.1-10 Hz band. We describe the plethora of potential astrophysical sources in this band and make estimates for their event rates and thereby, the sensitivity requirements for these detectors. The scientific payoff from measuring astrophysical gravitational waves in this frequency band is great. Although we find no fundamental limits to the detector sensitivity in this band, the remaining technical limits will be extremely challenging to overcome. [ABSTRACT FROM AUTHOR]

We show that nearly extremal Kerr black holes have two distinct sets of quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes (DMs). The ZDMs exist for all harmonic indices / and m ⩾0, and their frequencies cluster onto the real axis in the extremal limit. The DMs have nonzero damping for all black hole spins; they exist for all counterrotating modes (m < 0) and for corotating modes with 0 ⩽ μ ≲ μc = 0.74 (in the eikonal limit), where μ = m/(1 + 1/2). When the two families coexist, ZDMs and DMs merge to form a single set of quasinormal modes as the black hole spin decreases. Using the effective potential for perturbations of the Kerr spacetime, we give intuitive explanations for the absence of DMs in certain areas of the spectrum and for the branching of the spectrum into ZDMs and DMs at large spins. [ABSTRACT FROM AUTHOR]

When one splits spacetime into space plus time, the Weyl curvature tensor (which equals the Riemann tensor in vacuum) splits into two spatial, symmetric, traceless tensors: the tidal field ε, which produces tidal forces, and the frame-drag field B, which produces differential frame dragging. In recent papers, we and colleagues have introduced ways to visualize these two fields: tidal tendex lines (integral curves of the three eigenvector fields of ε) and their tendicities (eigenvalues of these eigenvector fields); and the corresponding entities for the frame-drag field: frame-drag vortex lines and their vorticities. These entities fully characterize the vacuum Riemann tensor. In this paper, we compute and depict the tendex and vortex lines, and their tendicities and vorticities, outside the horizons of stationary (Schwarzschild and Kerr) black holes; and we introduce and depict the black holes' horizon tendicity and vorticity (the normal-normal components of ε and B on the horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is proportional to the horizon's intrinsic scalar curvature, and the horizon vorticity is proportional to an extrinsic scalar curvature. We show that, for horizon-penetrating time slices, all these entities(ε,B, the tendex lines and vortex lines, the lines' tendicities and vorticities, and the horizon tendicities and vorticities) are affected only weakly by changes of slicing and changes of spatial coordinates, within those slicing and coordinate choices that are commonly used for black holes. We also explore how the tendex and vortex lines change as the spin of a black hole is increased, and we find, for example, that as a black hole is spun up through a dimensionless spin a/M = √3/2, the horizon tendicity at its poles changes sign, and an observer hovering or falling inward there switches from being stretched radially to being squeezed. At this spin, the tendex lines that stick out from the horizon's poles switch from reaching radially outward toward infinity to emerging from one pole, swinging poloidally around the hole and descending into the other pole. [ABSTRACT FROM AUTHOR]

Measurement-induced back-action, a direct consequence of the Heisenberg uncertainty principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al. [Phys. Rev. Lett. 108, 033602 (2012)], and show that the results of this experiment not only characterize the zero-point fluctuation of a near-ground-state nanomechanical oscillator, but also demonstrate the existence of quantum back-action noise--through correlations that exist between sensing noise and back-action noise. These correlations arise from the quantum coherence between the mechanical oscillator and the measuring device, which build up during the measurement process, and are key to improving sensitivities beyond the standard quantum limit [ABSTRACT FROM AUTHOR]