Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
arXiv:2503.24162 · doi: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.
24 pages, 3 figure, matches published version
References in corpus (17)
- Bondi-Sachs Formalism
- What happens at the horizon(s) of an extreme black hole?
- Hyperbolically symmetric static fluids: A general study
- Geodesics of the hyperbolically symmetric black hole
- Superradiance of a charged scalar field coupled to the Einstein-Maxwell equations
- Gravitational collapse of charged scalar fields
- Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
- The affine-null metric formulation of Einstein's equations
- The affine-null formulation of the gravitational equations: spherical case
- Revisiting timelike geodesics in the Fisher-Janis-Newman-Winicour-Wyman spacetime
- On asymptotically flat solutions of Einstein's equations periodic in time II. Spacetimes with scalar-field sources
- Strong Cosmic Censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry
- Simple, explicitly time-dependent and regular solutions of the linearized vacuum Einstein equations on a null cone
- Worldtube conservation laws for the null-timelike evolution problem
- The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions
- Bounds for Lyapunov exponent of circular light orbits in black holes
- Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates