One of the most exciting potential sources of gravitational waves for low-frequency, space-based gravitational wave (GW) detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such ''extreme mass ratio inspiral'' systems (EMRIs) and extraction of information from those waves require template waveforms. The systems' extreme mass ratio means that their waveforms can be determined accurately using black hole perturbation theory. Such calculations are computationally very expensive. There is a pressing need for families of approximate waveforms that may be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such kludge waveforms and describe ways to generate them. Different kinds of kludges have already been used to scope out data analysis issues for LISA. The models we study here are based on computing a particle's inspiral trajectory in Boyer-Lindquist coordinates, and subsequent identification of these coordinates with flat-space spherical polar coordinates. A gravitational waveform may then be computed from the multipole moments of the trajectory in these coordinates, using well-known solutions of the linearised gravitational perturbation equations in flat space time. We compute waveforms using a standard slow-motion quadrupole formula, a quadrupole/octupole formula, and a fast-motion, weak-field formula originally developed by Press. We assess these approximations by comparing to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglecting GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the final search of LISA data for EMRIs.

This paper presents a complete description of Virgo, the French-Italian gravitational wave detector. The detector, built at Cascina, near Pisa (Italy), is a very large Michelson interferometer, with 3 km-long arms. JINST 7 P03012In this paper, following a presentation of the physics requirements, leading to the specifications for the construction of the detector, a detailed description of all its different elements is given. These include civil engineering infrastructures, a huge ultra-high vacuum (UHV) chamber (about 6000 cubic metres), all of the optical components, including high quality mirrors and their seismic isolating suspensions, all of the electronics required to control the interferometer and for signal detection. The expected performances of these different elements are given, leading to an overall sensitivity curve as a function of the incoming gravitational wave frequency.This description represents the detector as built and used in the first data-taking runs. Improvements in different parts have been and continue to be performed, leading to better sensitivities. These will be detailed in a forthcoming paper.

After publication of the paper, minor typos were found in Eqs. (6) and (8). We correct these for completeness but note that no results in the paper were affected. Equation (6) should read z ÿ zz ÿ ÿ z z 2 ÿ zQ L 2 z a 2 1 ÿ E 2 Q;while Eq. (8) should read d dt 1 ÿ E 2 p p ÿ r 3 1 ÿ e ÿ ep r 3 1 ÿ e cos 1=2 p ÿ r 4 1 e ep ÿ r 4 1 e cos 1=2 a 2 Ez1 ÿ e 2 : (8) PHYSICAL REVIEW D 77, 049902(E) (2008) 1550-7998= 2008=77(4)=049902(1) 049902-1

We describe the possibility of using the laser interferometer space antenna (LISA) 's gravitational-wave observations to study, with high precision, the response of a massive central body (e.g. a black hole or a soliton star) to the tidal gravitational pull of an orbiting, compact, small-mass object (a white dwarf, neutron star, or small-mass black hole). Motivated by this LISA application, we use first-order perturbation theory to study tidal coupling for a special, idealized case: a Schwarzschild black hole of mass M, tidally perturbed by a ''moon'' with mass M in a circular orbit at a radius b M with orbital angular velocity . We investigate the details of how the tidal deformation of the hole gives rise to an induced quadrupole moment I ij in the hole's external gravitational field at large radii, including the vicinity of the moon. In the limit that the moon is static, we find, in Schwarzschild coordinates and ReggeWheeler gauge, the surprising result that there is no induced quadrupole moment. We show that this conclusion is gauge dependent and that the static, induced quadrupole moment for a black hole is inherently ambiguous, and we contrast this with an earlier result of Suen, which gave, in a very different gauge, a nonzero static induced quadrupole moment with a sign opposite to what one would get for a fluid central body. For the orbiting moon and the central Schwarzschild hole, we find (in agreement with a recent result of Poisson) a time-varying induced quadrupole moment that is proportional to the time derivative of the moon's tidal field, I ij 32=45 M 6 _ E ij and that therefore is out of phase with the tidal field by a spatial angle =4 and by a temporal phase shift =2. This induced quadrupole moment produces a gravitational force on the moon that reduces its orbital energy and angular momentum at the same rate as the moon's tidal field sends energy and angular momentum into the hole's horizon. As a partial analog of a result derived long ago by Hartle for a spinning hole and a static distant companion, we show that the orbiting moon's tidal field induces a tidal bulge on the hole's horizon, and that the rate of change of the horizon shape (i.e. the horizon shear) leads the perturbing tidal field at the horizon by an angle 4M . We prefer to avoid introducing an ingoing null geodesic, as Hartle did in his definition of the phase shift, because the moon is in the central body's near zone (b 1= ) and thus should interact with the horizon instantaneously, not causally. We discuss the implications of these results for LISA's future observations of tidal coupling, including the inappropriateness of using the concepts of tidal polarizability and tidal lag or lead angle, for the massive central body, when discussing LISA's observations.

We explore prospects for detecting gravitational waves from stellar-mass compact objects spiraling into intermediate mass black holes (BHs) (M 50M to 350M ) with ground-based observatories. We estimate a rate for such intermediate-mass-ratio inspirals of &1-30 yr ÿ1 in Advanced LIGO. We show that if the central body is not a BH but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat, then the waves will likely be triperiodic, as for a BH. We suggest that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) details of the central body's metric, the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. We estimate that advanced ground-based detectors can constrain central body deviations from a BH with interesting accuracy. [3] and its international partners will increase the volume of the Universe searched a thousandfold or more. The most promising GW sources for this network are the inspiral and coalescence of black hole (BH) and/or neutron star (NS) binaries. Current inspiral searches target sources with total mass M & 40M : NS binaries with masses 1-3M , BH binaries with masses 3-40M , and NS-BH binaries with components in these mass ranges [4,5].Ultraluminous x-ray observations and simulations of globular cluster dynamics suggest the existence of intermediate-mass black holes (IMBHs) with masses M 10 2 -10 4 M [6]. The GWs from the inspiral of a NS or stellar-mass BH into an IMBH with mass M 50-350M will lie in the frequency band of AdvLIGO. These intermediate-mass-ratio inspirals (IMRIs) are analogous to the extreme-mass-ratio inspirals (EMRIs) of 10M objects spiraling into 10 6 M BHs, targeted by the planned LISA observatory [7]. We consider IMRIs containing NSs and BHs, as less compact objects (e.g., white dwarfs) are tidally disrupted at frequencies too low to be detectable in AdvLIGO.If we consider the possibility that the central body of an IMRI (or EMRI) is not a BH, but some other general relativistic object (e.g., a boson star or a naked singularity [8]), then we can quantify the accuracy with which it has the properties predicted for a BH that: (i) it obeys the BH no-hair theorem (its spacetime geometry is the Kerr metric, fully determined by its mass and spin), and (ii) its tidal coupling (tide-induced transfer of energy and angular momentum between orbit and body) agrees with BH predictions. Searching for non-BH objects may yield an unexpected discovery.We report on our initial explorations of the prospects for detecting GWs from IMRIs and probing the properties of IMRIs' central bodies. We report (i) IMRI event rate estimates in AdvLIGO, (ii) estimates of the efficacy of GW template families for IMRI searches, (iii) explorations of the character of the IMRI (EMRI) waves if the central body is not a BH, (iv) generalizations of Ryan's theorem concerning the information about the central body carried by IMRI and EMRI w...