Hierarchical formulation of the self-gravitating, n-dimensional, charged scalar field in spherical symmetry in affine null formalism

2026/06/30 by Laura Bridera, Emanuel Gallo, Thomas Mädler
Physics and Astronomy · #gr-qc

paper · pdf · doi:10.1007/s10714-026-03592-5

Abstract

We develop an affine-null characteristic formulation of the Einstein-Maxwell system coupled to a charged complex scalar field in n-dimensional spherical symmetry. By introducing suitable auxiliary variables, the main field equations are cast into a hierarchical system of radial hypersurface equations, supplemented by a transport equation for the scalar field. We discuss the associated characteristic initial-boundary value problem for asymptotic, vertex and null-boundary configurations, and derive the corresponding asymptotic quantities and balance laws. As a consistency check, we recover the scalar-free Reissner-Nordström-Tangherlini family, including both the non-extremal and extremal branches, directly from the hierarchy. The resulting framework provides a systematic setting for the study of charged scalar dynamics and exact black-hole solutions in higher-dimensional affine-null coordinates.

Citations

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• Angle of null energy condition lines in critical spacetimes
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• Spherically symmetric black holes and affine-null metric formulation of Einstein's equations
• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
• Conformal compactification and affine-null metric formulation of the Einstein equations

Related

• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
• Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates
• Affine-null formulation of the gravitational equations: Spherical case
• Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates
• Simulations of gravitational collapse in null coordinates IV: evolving through the event horizon, with an application to the spherical charged scalar field