Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr

Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric

Published:2021-06 Issue:02 Volume:18 Page:293-310
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

Besset Nicolas¹,Häfner Dietrich²

Affiliation:

1. Laboratoire Analyse Géométrie Modélisation, Cergy Paris Université, 2 Av. Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

2. Institut Fourier, Université Grenoble Alpes, 100 Rue Des Maths, 38610 Gières, France

Abstract

We show the existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the De Sitter–Kerr–Newman metric for small charge and mass of the field and small angular momentum of the black hole. The mechanism behind is that the zero resonance that exists for zero charge, mass and angular momentum moves into the upper half plane.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219891621500090

Reference15 articles.

1. Decay of the Local Energy for the Charged Klein–Gordon Equation in the Exterior De Sitter–Reissner–Nordström Spacetime

2. Decay and Non-Decay of the Local Energy for the Wave Equation on the De Sitter–Schwarzschild Metric

3. Strong cosmic censorship in charged black-hole spacetimes: Still subtle

4. Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole

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