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Compact objects observed via gravitational waves are classified as black holes or neutron stars primarily based on their inferred mass with respect to stellar evolution expectations. However, astrophysical expectations for the lowest mass range, ≲1.2⁢𝑀⊙, are uncertain. If such low-mass compact objects exist, ground-based gravitational wave detectors may observe them in binary mergers. Lacking astrophysical expectations for classifying such observations, we go beyond the mass and explore the role of tidal effects. We evaluate how combined mass and tidal inference can inform whether each binary component is a black hole or a neutron star based on consistency with the supranuclear-density equation of state. Low-mass neutron stars experience a large tidal deformation; its observational identification (or lack thereof) can therefore aid in determining the nature of the binary components. Using simulated data, we find that the presence of a sub-solar mass neutron star (black hole) can be established with odds ∼100∶1 when two neutron stars (black holes) merge and emit gravitational waves at signal-to-noise ratio ∼20. For the same systems, the absence of a black hole (neutron star) can be established with odds ∼10∶1. For mixed neutron star-black hole binaries, we can establish that the system contains a neutron star with odds ≳5∶1. Establishing the presence of a black hole in mixed neutron star-black hole binaries is more challenging, except for the case of a ≲1⁢𝑀⊙ black hole with a ≳1⁢𝑀⊙ neutron star companion. On the other hand, classifying each individual binary component suffers from an inherent labeling ambiguity. 

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse.We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.