Collapsing objects with the same gravitational trajectory can radiate away different amount of energy

Abstract

We study radiation emitted during the gravitational collapse from two different types of shells. We assume that one shell is made of dark matter and is completely transparent to the test scalar (for simplicity) field which belongs to the standard model, while the other shell is made of the standard model particles and is totally reflecting to the scalar field. These two shells have exactly the same mass, charge and angular momentum (though we set the charge and angular momentum to zero), and therefore follow the same geodesic trajectory. However, we demonstrate that they radiate away different amount of energy during the collapse. This difference can in principle be used by an asymptotic observer to reconstruct the physical properties of the initial collapsing object other than mass, charge and angular momentum. This result has implications for the information paradox and expands the list of the type of information which can be released from a collapsing object.