The tidal gap: causality bound on exotic compact objects with applications in the solar and sub-solar mass range

Abstract: In this work, we highlight the existence of a lower limit on the tidal deformability parameter $Λ$, determined by the requirement of relativistic causality. Additionally, by considering the upper bound set on compactness, we identify the region within the parameter space of compactness versus tidal deformability, where physically motivated exotic compact objects (ECOs) could potentially reside. Our analysis reveals the presence of a tidal gap between black holes, characterized by vanishing tidal deformability, and physically motivated ECOs. Prompted by this finding, we investigate the possibility that a population of maximally compact exotic objects, described by a linear equation of state (EoS), may simultaneously inhabit the lower mass gap and the sub-solar region, thus qualifying as (primordial) black hole mimickers while distinguishing themselves from the latter by their non-zero tidal deformability. Finally, considering the case of solitonic boson stars as proxies for ECOs described by a linear EoS, we discuss how it is possible to further reduce the lower limit on $Λ$, provided that the strong energy condition is violated (but not the dominant energy condition, and therefore causality).