The Maxwell-scalar field system near spatial infinity
The Maxwell-scalar field system near spatial infinity
We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of non-linearities of this system on the regularity of solutions and polyhomogeneous expansions at null infinity and, in particular, at the critical sets where null infinity touches spatial infinity. The main outcome from our analysis is that the nonlinear interaction makes both fields more singular at the conformal boundary than what is seen when the fields are non-interacting. In particular, we find a whole new class of logarithmic terms in the asymptotic expansions, which depend on the coupling constant between the Maxwell and scalar fields. We analyze the implications of these results on the peeling (or rather lack thereof) of the fields at null infinity.
Minucci, Marica
97caac7b-bef9-4489-ba0e-98e8c3fabc39
Panosso Macedo, Rodrigo
8f176eb4-ca20-492b-a41e-e78d47d6fefe
Valiente-Kroon, Juan
22b0ab11-80a1-47fa-811c-61d5c549a356
Minucci, Marica
97caac7b-bef9-4489-ba0e-98e8c3fabc39
Panosso Macedo, Rodrigo
8f176eb4-ca20-492b-a41e-e78d47d6fefe
Valiente-Kroon, Juan
22b0ab11-80a1-47fa-811c-61d5c549a356
Minucci, Marica, Panosso Macedo, Rodrigo and Valiente-Kroon, Juan
(2022)
The Maxwell-scalar field system near spatial infinity.
J.Math.Phys., 63 (8), [082501].
(doi:10.1063/5.0104602).
Abstract
We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of non-linearities of this system on the regularity of solutions and polyhomogeneous expansions at null infinity and, in particular, at the critical sets where null infinity touches spatial infinity. The main outcome from our analysis is that the nonlinear interaction makes both fields more singular at the conformal boundary than what is seen when the fields are non-interacting. In particular, we find a whole new class of logarithmic terms in the asymptotic expansions, which depend on the coupling constant between the Maxwell and scalar fields. We analyze the implications of these results on the peeling (or rather lack thereof) of the fields at null infinity.
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2206.04366
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Accepted/In Press date: 31 July 2022
e-pub ahead of print date: 29 August 2022
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Local EPrints ID: 471479
URI: http://eprints.soton.ac.uk/id/eprint/471479
ISSN: 0022-2488
PURE UUID: 5ae666e2-367d-4dbd-90e5-27125420ff51
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Date deposited: 09 Nov 2022 17:33
Last modified: 17 Mar 2024 04:09
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Author:
Marica Minucci
Author:
Juan Valiente-Kroon
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