Bondi-spherically symmetric Einstein-non-linear scalar field system

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-05-13 DOI:10.1016/j.geomphys.2025.105529

Franck Modeste Teyang , Pierre Noundjeu , David Tegankong

引用次数: 0

Abstract

The study of Einstein's equations coupled with a nonlinear scalar field and a positive cosmological constant provides deeper insight into the physics of the large-scale universe. It also serves as a means to test theoretical models against cosmological observations. In this paper, we consider a characteristic initial value problem defined on a future isotropic cone for Einstein's equations coupled with a nonlinear scalar field and a positive cosmological constant in a Bondi-spherically symmetric spacetime. We establish that, for small initial data, this system possesses a unique global solution in Bondi time, which is causally complete in the future. Additionally, we prove that this solution decays exponentially over time and approaches the de Sitter solution. Consequently, our results provide a nonlinear stability result for de Sitter spacetime within the considered class of solutions, and they also support the cosmic no-hair conjecture.

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邦迪-球对称爱因斯坦-非线性标量场系统

对爱因斯坦方程与非线性标量场和正宇宙常数耦合的研究，为大规模宇宙的物理学提供了更深入的见解。它还可以作为检验理论模型与宇宙观测结果的一种手段。本文研究了在bondi -球对称时空中，具有非线性标量场和正宇宙学常数的爱因斯坦方程在未来各向同性锥上的特征初值问题。我们建立了对于小的初始数据，该系统在邦迪时间内具有唯一的全局解，在未来是因果完备的。此外，我们证明了该解随时间呈指数衰减并接近de Sitter解。因此，我们的结果在考虑的解类中提供了de Sitter时空的非线性稳定性结果，并且它们也支持宇宙无毛猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity