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.
Highlights
In Einstein-Maxwell theory a stationary black hole solution is generally characterized by its mass, electric charge and angular momentum
In Einstein-Maxwell theory, physical properties of a black hole are completely determined by its mass, electric charge and angular momentum
There is no additional information left after a black hole is formed
Summary
We consider a freely falling massive spherical shell. The time dependent radius of the shell is R(τ ), where τ is the proper time of the observer located on the shell. The geometry outside the shell is Schwarzschild ds2 = − 1 − 2M dt2 + r dΩ = dθ2 + sin θdφ. The geometry inside the shell is by the Birkhoff theorem flat Minkowski space ds2 = −dT 2 + dr2 + r2dΩ (3). The motion of the shell can be found by matching the geometry inside and outside the shell [10]. The equation of motion is given in terms of the conserved quantity μ, which is just the rest mass of the shell
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