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arXiv 2403.07550gr-qcastro-ph.CO
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后准静态近似:一种引力坍缩的解析方法

The post--quasi-static approximation: An analytical approach to gravitational collapse

L. Herrera, A. Di prisco, J. Ospino

AI总结:

本研究改进了后准静态近似下描述引力坍缩的半数值方法,通过施加复杂度因子为零的条件实现基本微分方程的解析积分,排除了同/准同演化及绝热演化的可行性,结合可观测量或启发式假设提出两个受经典解启发的物理模型。

摘要:

多年前提出的一种用于在后准静态近似下描述引力坍缩的半数值方法得到了改进,目的是避免对该方法所基于的基本微分方程进行数值积分。为此,我们必须对流体分布施加一些限制。更具体地说,我们将假设复杂度因子为零的条件,该条件允许对相关微分方程进行解析积分,并得出具有物理意义的模型。相反,我们证明同演化和准同演化均不可接受,因为它们会导致测地流体,而测地流体不适合在后准静态近似下描述。此外,我们还证明,在该近似框架内,绝热演化也会导致测地流体,因此我们将仅考虑耗散系统。除了复杂度因子为零的条件外,还需要额外信息才能完整描述模型。我们将提出获取此类信息的不同策略,这些策略基于可观测量(例如光度和红移),和/或启发式数学假设。为了说明该方法,我们提出了两个模型。一个模型受著名的Schwarzschild内部解启发,另一个受Tolman VI解启发。

英文摘要:

A semi--numerical approach proposed many years ago for describing gravitational collapse in the post--quasi--static approximation, is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi--homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post--quasi--static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids and therefore we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g. luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

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