Narrow resonances and black-hole-like absorption in a non-black-hole metric

A massive body with the Schwarzschild interior metric (perfect fluid of constant density) develops a pressure singularity at the origin when the radius of the body $R$ approaches $9r_s/8$, where $r_s$ is the Schwarzschild radius. We show that a quantum scalar particle scattered in this gravitational field possesses a dense spectrum of narrow resonances. Their density and lifetimes tend to infinity in the limit $R\rightarrow 9r_s/8$, and we determine the cross section of the particle capture into these quasibound states. Therefore, a body that is not a black hole demonstrates black-hole-like absorption.