A Positive-Definite Energy Functional for Axially Symmetric Maxwell's Equations on Kerr-de Sitter Black Hole Spacetimes

Abstract

We prove that there exists a phase space of canonical variables for the initial value problem for axially symmetric Maxwell fields propagating in Kerr-de Sitter black hole spacetimes such that their motion is restricted to the level sets of a positive-definite Hamiltonian, despite the ergo-region.

Journal version

References in corpus (3)

• The global non-linear stability of the Kerr-de Sitter family of black holes
• On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry
• Decay of Solutions to the Maxwell Equations on Schwarzschild-de Sitter Spacetimes

Cited by in corpus (5)

• Price's law for spin fields on a Schwarzschild background
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy
• Sharp decay for Teukolsky equation in Kerr spacetimes
• Axially Symmetric Perturbations of Kerr Black Holes II: Boundary Behaviour of the Dynamics in the Orbit Space