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 → 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.