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Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes

Natário, José and Sasane, Amol (2021) Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. ISSN 0246-0203 (In Press)

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Abstract

The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in at Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in at FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.

Item Type: Article
Official URL: https://projecteuclid.org/journals/annales-de-lins...
Additional Information: © 2021 Association des Publications de l’Institut Henri Poincaré
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 10 Nov 2021 15:33
Last Modified: 17 Nov 2021 01:12
URI: http://eprints.lse.ac.uk/id/eprint/112584

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