Entire spherically symmetric spacelike graphs with prescribed mean curvature function in Schwarzschild and Reissner–Nordström spacetimes

DOI10.1088/0264-9381/32/3/035018zbMath1312.83007OpenAlexW2015925244MaRDI QIDQ5179094

Daniel de la Fuente, Alfonso Romero, Pedro J. Torres

Publication date: 19 March 2015

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0264-9381/32/3/035018

zbMATH Keywords

quasilinear elliptic equationSchwarzschild spacetimeDirichlet boundary conditionsingular \(\phi\)-Laplacianprescribed mean curvature functionReissner-Nordström spacetime

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Black holes (83C57) Wave equation (35L05) Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Space-time singularities, cosmic censorship, etc. (83C75) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Exact solutions to problems in general relativity and gravitational theory (83C15) Einstein-Maxwell equations (83C22) Quasilinear elliptic equations with mean curvature operator (35J93)

Related Items (6)

On a prescribed mean curvature equation in Lorentz-Minkowski space ⋮ Global structure of a nodal solutions set of mean curvature equation in static spacetime ⋮ Global bifurcation of solutions of the mean curvature spacelike equation in certain standard static spacetimes ⋮ The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz-Minkowski space ⋮ Corrigendum: Entire spherically symmetric spacelike graphs with prescribed mean curvature function in Schwarzschild and Reissner–Nordström spacetimes (2015 Class. Quantum Grav . 32 035018) ⋮ Constructing graphs over \(\mathbb R^n\) with small prescribed mean-curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space
• Spacelike hypersurfaces with prescribed boundary values and mean curvature
• H-surfaces in Lorentzian manifolds
• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space
• Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space
• Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
• Ground state solution for a problem with mean curvature operator in Minkowski space
• Radial solutions for some nonlinear problems involving mean curvature operators in Euclidean and Minkowski spaces
• General Relativity for Mathematicians

This page was built for publication: Entire spherically symmetric spacelike graphs with prescribed mean curvature function in Schwarzschild and Reissner–Nordström spacetimes