Advanced gravitational wave detectors, currently under construction, are expected to directly observe gravitational wave signals of astrophysical origin. The Einstein Telescope, a third-generation gravitational wave detector, has been proposed in order to fully open up the emerging field of gravitational wave astronomy. In this article we describe sensitivity models for the Einstein Telescope and investigate potential limits imposed by fundamental noise sources. A special focus is set on evaluating the frequency band below 10Hz where a complex mixture of seismic, gravity gradient, suspension thermal and radiation pressure noise dominates. We develop the most accurate sensitivity model, referred to as ET-D, for a third-generation detector so far, including the most relevant fundamental noise contributions.

The space-based Laser Interferometer Space Antenna (LISA) will be able to observe the gravitational-wave signals from systems comprised of a massive black hole and a stellar-mass compact object. These systems are known as extreme-mass-ratio inspirals (EMRIs) and are expected to complete $\sim 10^4–10^5$ cycles in band, thus allowing exquisite measurements of their parameters. In this work, we attempt to quantify the astrophysical uncertainties affecting the predictions for the number of EMRIs detectable by LISA, and find that competing astrophysical assumptions produce a variance of about three orders of magnitude in the expected intrinsic EMRI rate. However, we find that irrespective of the astrophysical model, at least a few EMRIs per year should be detectable by the LISA mission, with up to a few thousands per year under the most optimistic astrophysical assumptions. We also investigate the precision with which LISA will be able to extract the parameters of these sources. We find that typical fractional statistical errors with which the intrinsic parameters (redshifted masses, massive black hole spin and orbital eccentricity) can be recovered are $\sim {10}^{-6}–{10}^{-4}$. Luminosity distance (which is required to infer true masses) is inferred to about 10% precision and sky position is localized to a few square degrees, while tests of the multipolar structure of the Kerr metric can be performed to percent-level precision or better.

Black hole binaries with extreme ($\gtrsim 10^4:1$) or intermediate ($\sim 10^2-10^4:1$) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed Laser Interferometer Space Antenna. These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis, and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany.

This document introduces the exciting and fundamentally new science and astronomy that the European New Gravitational Wave Observatory (NGO) mission (derived from the previous LISA proposal) will deliver. The mission (which we will refer to by its informal name ``eLISA) will survey for the first time the low-frequency gravitational wave band (about 0:1 mHz to 1 Hz), with sufficient sensitivity to detect interesting individual astrophysical sources out to z = 15. The measurements described here will address the basic scientific goals that have been captured in ESAs ``New Gravitational Wave Observatory Science Requirements Document; they are presented here so that the wider scientific community can have access to them. The eLISA mission will discover and study a variety of cosmic events and systems with high sensitivity: coalescences of massive black holes binaries, brought together by galaxy mergers; mergers of earlier, less-massive black holes during the epoch of hierarchical galaxy and black-hole growth; stellar-mass black holes and compact stars in orbits just skimming the horizons of massive black holes in galactic nuclei of the present era; extremely compact white dwarf binaries in our Galaxy, a rich source of information about binary evolution and about future Type Ia supernovae; and possibly most interesting of all, the uncertain and unpredicted sources, for example relics of inflation and of the symmetry-breaking epoch directly after the Big Bang. eLISAs measurements will allow detailed studies of these signals with high signal-to-noise ratio, addressing most of the key scientific questions raised by ESAs Cosmic Vision programme in the areas of astrophysics and cosmology. They will also provide stringent tests of general relativity in the strong-field dynamical regime, which cannot be probed in any other way. This document not only describes the science but also gives an overview on the mission design and orbits. LISAs heritage in the eLISA design will be clear to those familiar with the previous proposal, as will its incorporation of key elements of hardware from the LISA Pathfinder mission, scheduled for launch by ESA in 2014. But eLISA is fundamentally a new mission, one that will pioneer the completely new science of low-frequency gravitational wave astronomy