  At the dawn of a golden age for gravitational wave astronomy, we must leave
no stone unturned in our quest for new phenomena beyond our current
understanding of General Relativity (GR), particle physics and nuclear physics.
In this paper we discuss gravitational echoes from ultracompact stars. We
restrict our analysis to exact solutions of Einstein field equations in GR that
are supported by physically motivated equations of state (EoS), and in
particular we impose the constraint of causality. Our main conclusion is that
ultracompact objects supported by physical EoS are not able to generate
gravitational echoes like those that characterize the relaxation phase of a
putative black hole mimicker. Nevertheless, we identify a class of physical
exotic objects that are compact enough to accommodate the presence of an
external unstable light ring, thus opening the possibility of trapping
gravitational radiation and affecting the ringdown phase of a merger event.
Most importantly, we show that once rotation is included these stars --
contrary to what usually expected for ultracompact objects -- are not plagued
by any ergoregion instability. We extend our analysis for arbitrary values of
angular velocity up to the Keplerian limit, and we comment about potential
signals relevant for gravitational wave interferometers.
