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 · #Affine transformation #Circular symmetry #Cosmology and Gravitation Theories #Differential geometry #Formalism (music) #Pulsars and Gravitational Waves Research #Scalar field #Statistical Mechanics and Entropy #Symmetry (geometry) #gr-qc

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

published in General Relativity and Gravitation 58(8) (Springer Science+Business Media)

openalex publication_date 2026/07/24 · openalex created_date 2026/07/25 · openalex updated_date 2026/08/05

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

• The four laws of black hole mechanics
• Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie
• Charged scalar gravitational collapse in de Sitter spacetime
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Affine-null metric formulation of General Relativity at two intersecting null hypersurfaces
• The affine-null formulation of the gravitational equations: spherical case
• Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates
• Simulations of gravitational collapse in null coordinates. I. Formulation and weak-field tests in generalized Bondi gauges
• Simulations of gravitational collapse in null coordinates. II. Critical collapse of an axisymmetric scalar field
• Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates
• Angle of null energy condition lines in critical spacetimes
• Simulations of gravitational collapse in null coordinates. IV. Evolving through the event horizon, with an application to the spherical charged scalar field
• 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
• The 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