Formulating the complete initial boundary value problem in numerical relativity to model black hole echoes

          @misc{ pirsa_PIRSA:24070092,
            doi = {10.48660/24070092},
            url = {https://pirsa.org/24070092},
            author = {Dailey, Conner},
            keywords = {},
            language = {en},
            title = {Formulating the complete initial boundary value problem in numerical relativity to model black hole echoes},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {jul},
            note = {PIRSA:24070092 see, \url{https://pirsa.org}}
          }
          

Abstract

Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before reaching the horizon. There does not seem to be a good understanding of how to properly model a reflecting surface in numerical relativity, as the vast majority of the literature avoids the implementation of artificial boundaries, or applies transmitting boundary conditions. Here, we present a framework for reflecting a scalar field in a fully dynamical spherically symmetric spacetime, and implement it numerically. We study the evolution of a wave packet in this situation and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole. This opens the door to model exotic near-horizon physics within full numerical relativity.