A scattering theory for linear waves on the interior of Reissner-Nordstr\"om black holes

Understand

We develop a scattering theory for the linear wave equation $\Box_g \psi = 0$ on the interior of Reissner-Nordstr\"om black holes, connecting the fixed frequency picture to the physical space picture.

• Our main result gives the existence, uniqueness and asymptotic completeness of finite energy scattering states.
• The past and future scattering states are represented as suitable traces of the solution $\psi$ on the bifurcate event and Cauchy horizons.
• The heart of the proof is to show that after separation of variables one has uniform boundedness of the reflection and transmission coefficients of the resulting radial o.d.e.