关于爱因斯坦-克莱因-戈登系统的傅立叶分析：傅立叶常数的增长与衰减

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2023-12-09 DOI:10.1007/s00023-023-01393-z

Athanasios Chatzikaleas

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引用次数: 0

摘要

我们考虑了负宇宙常数与球对称无质量标量场耦合的（（1+3））维爱因斯坦方程，并研究了反德西特时空周围的扰动。我们推导了共振系统，挑出了消失的世俗项，并讨论了与小除数有关的问题。最重要的是，我们严格确定了所有相互作用系数的渐近行为（在大多数情况下是尖锐的）。后者基于与线性化算子相关的特征函数的统一估计以及一些振荡积分。

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On the Fourier Analysis of the Einstein–Klein–Gordon System: Growth and Decay of the Fourier Constants

We consider the \((1+3)\)-dimensional Einstein equations with negative cosmological constant coupled to a spherically symmetric, massless scalar field and study perturbations around the anti-de Sitter spacetime. We derive the resonant systems, pick out vanishing secular terms and discuss issues related to small divisors. Most importantly, we rigorously establish (sharp, in most of the cases) asymptotic behaviour for all the interaction coefficients. The latter is based on uniform estimates for the eigenfunctions associated to the linearized operator as well as on some oscillatory integrals.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.