The advent of space-based gravitational-wave detectors like the Laser Interferometer Space Antenna will allow us to observe signals, most of which are expected to be emitted by white-dwarf binaries. Among these systems another kind of compact objects could be hidden, postulated by Glendenning, Kettner, and Weber in 1995, containing a small core made of strange quark matter surrounded by layers of hadronic matter reaching densities much higher than in white dwarfs. These so-called strange dwarfs cannot be easily distinguished from white dwarfs through electromagnetic observations alone; their outermost envelopes are expected to have the same composition and their radii are quite similar (except for low masses). However, future measurements of the tidal deformability through gravitational-wave observations could provide a new way to reveal their existence. In this paper, we revisit the structure and the tidal deformability of strange dwarfs in full general relativity taking into account the possible crystallization of their envelope. Unlike most previous studies, we do not describe the hadronic layers using the equation of state of Baym, Pethick, and Sutherland, which was originally designed for the outer crust of a neutron star. The conditions leading to such heavy elements in gravitational-core collapse supernova explosions are not expected to be met during the stellar evolution leading to the formation of strange dwarfs. Instead, we consider the same light elements as found in white dwarfs but we take into account electron captures by nuclei and possibly pycnonuclear fusions that may be triggered by compression. We find that the radius of strange dwarfs is systematically smaller than that of their white dwarf relatives. These deviations can be large for very low-mass stars but mostly lie within the current observational uncertainties for typical white dwarf masses. On the other hand, the observable tidal deformability coefficient <math display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> is strongly reduced in comparison to white dwarfs and the deviation will be potentially measurable by future space-based gravitational-wave detectors.< Leer menos