Echoes of compact objects: new physics near the surface and matter at a distance

It is well known that a hypothetical compact object that looks like an Einsteinian (Schwarzschild or Kerr) black hole everywhere except a small region near its surface should have the ringdown profile predicted by the Einstein theory at early and intermediate times, but modified by the so-called echoes at late times. A similar phenomenon appears when one considers an Einsteinian black hole and a shell of matter placed at some distance from it, so that astrophysical estimates could be made for the allowed mass of the black hole environment. While echoes for both systems have been extensively studied recently, no such analysis has been done for a system featuring phenomena simultaneously, that is, echoes due to new physics near the surface/event horizon and echoes due to matter at some distance from the black hole. Here, following [9, 11], we consider a traversable wormhole obtained by identifying two Schwarzschild metrics with the same mass M at the throat, which is near the Schwarzschild radius, and add a nonthin shell of matter at a distance. This allows us to understand how the echoes of the surface of the compact object are affected by the astrophysical environment at a distance. The straightforward calculations for the time-domain profiles of such a system support the expectations that if the echoes are observed, they should most probably be ascribed to some new physics near the event horizon rather than some "environmental" effect.