Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
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| Format: | Preprint |
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2025
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| _version_ | 1866915383760388096 |
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| author | Mädler, Thomas Gannouji, Radouane Gallo, Emanuel |
| author_facet | Mädler, Thomas Gannouji, Radouane Gallo, Emanuel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_24162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry Mädler, Thomas Gannouji, Radouane Gallo, Emanuel General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.24162 |