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

Understand

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.