Accretion of a Phantom Scalar Field by a Black Hole: restrictions on the field distribution

Using numerical simulations we study the accretion of a phantom scalar field into a black hole and track the black hole horizon shrinking process. We integrate the amount of field left outside the black hole during the process in terms of the properties of the wave packet sent toward the black hole. Our results indicate that the accretion of thick wave packets with small wave number is inefficient and a portion of the scalar field remains outside the black hole.