Beijing Institute of Mathematical Sciences and Applications

We will examine the stability problem of Reissner-Nordstrom black holes for the spherically symmetric Einstein-Maxwell-real scalar field system. We will start with the analysis of spherically symmetric linear waves on the exterior of Reissner-Nordstrom spacetimes. We will define and study basic properties of the Einstein-Maxwell-real scalar field system of equations under the assumption of spherical symmetry in the double null gauge. We will then study the stability problem of the full family of Reissner-Nordstrom black holes in this context.