Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
Phys. Rev. D 111, 124015 – Published 11 June, 2025
DOI: https://doi.org/10.1103/f5fc-zpld
Abstract
The characteristic initial boundary problem is discussed in spherical symmetry for the Einstein-Maxwell-scalar field equations. It is formulated for an affine-null metric, and the resulting field equations are cast into a hierarchical system of partial differential equations. The initial boundary value problem for a family of null hypersurfaces is specified for a timelike-null foliation at the central geodesic of spherical symmetry as well as for a double-null foliation where the corresponding boundary is a null hypersurface. For the latter, two distinct boundary value formulations arise: one where the null boundary has zero Misner-Sharp mass, and another one where the corresponding Misner-Sharp mass is nonzero. As an application, the nonextremal and the extremal Reissner-Nordström solution in null coordinates for a charged black hole and the Fisher-Janis-Newman-Winicour solution are derived.
