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

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.

References in corpus (21)

• Critical phenomena in gravitational collapse
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Bondi-Sachs Formalism
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Critical Behaviour and Universality in Gravitational Collapse of a Charged Scalar Field
• On Choptuik's scaling in higher dimensions
• Charge scaling and universality in critical collapse
• Self-Similar Collapse of Scalar Field in Higher Dimensions
• Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse
• Choptuik scaling in six dimensions
• 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
• Charged scalar gravitational collapse in de Sitter spacetime
• Simulations of gravitational collapse in null coordinates: II. Critical collapse of an axisymmetric scalar field
• Higher Dimensional Choptuik Scaling in Painleve Gullstrand Coordinates
• Simulations of gravitational collapse in null coordinates: I. Formulation and weak-field tests in generalised Bondi gauges
• Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates
• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
• Critical spacetime crystals in continuous dimensions
• Conformal compactification and affine-null metric formulation of the Einstein equations