放松TOV方程得到的压强剖面界
Pressure profile bounds from relaxing the TOV equation
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中文总结 AI 辅助
该研究通过放松TOV方程得到广义相对论理想流体球压强剖面的若干新通用界，分析了界的强度、假设弱度与分析易处理性的权衡，明确了界的依赖条件及与过往研究的关联。
中文摘要 AI 辅助
我们基于多种放松TOV常微分方程组的方式，得到了广义相对论理想流体球内部压强剖面的若干新的、相当通用的界，以此获得若干不同的微分不等式。与通常情况一样，界的强度、输入假设的弱度与分析的易处理性之间存在权衡关系。具体而言，我们将推导出若干直接但非平凡的界，这些界分别仅依赖于密度的正性、密度的有界性、密度的单调性或平均密度的单调性。我们将仔细地将这些新界置于该领域过往研究的历史框架中，并探讨它们之间的相互关联方式。
英文摘要
We develop several new and quite general bounds on the internal pressure profiles of general relativistic perfect fluid spheres --- based on various ways of relaxing the TOV system of ODEs to obtain several distinct differential inequalities. There is, as usual, a trade-off between strength of the bound, weakness of the input assumptions, and tractability of the analysis. Specifically we shall develop several straightforward but nontrivial bounds that variously depend only on the positivity of density, the boundedness of density, the monotonicity of density, or the monotonicity of the average density. We shall carefully place these new bounds within the historical framework of previous efforts in this regard, and explore the ways in which they are inter-related.
