In a recent work we explored the backreaction of a self-gravitating system of elementary neutral fermions at finite temperature in asymptotically AdS space, known as the "holographic neutron star". Such study was carried out by solving the Tolman-Oppenhemier-Volkoff equations under a perfect fluid assumption for the fermionic equation of state, accounting for both relativistic and finite temperature effects. Novel "dense core - diluted halo" density profiles in the AdS bulk were found, with corresponding two-point scalar field correlators obtained within the world line formalism, as a probe of the dual field theory. In this work we cover a much broader free parameter-space of the fermionic solutions in the bulk (from dilute to highly degenerate regime including for the critical point of gravitational collapse), and study their thermodynamic stability by calculating the grand canonical potential and free entropy. Such a stability analysis is performed using the Katz criterion, a technique historically applied to study the gravothermal catastrophe proper of classical self-gravitating systems in flat space. We identify some characteristic features of the unstable regions, both from the bulk and boundary perspectives, that can be used as proxies to detect instabilities on this kind of self-gravitating systems.

中文翻译：

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全息中子星在有限温度下的热力学不稳定性

在最近的一项工作中，我们探索了在有限温度下渐近 AdS 空间中基本中性费米子自引力系统的反向反应，称为“全息中子星”。此类研究是通过在费米子状态方程的完美流体假设下求解 Tolman-Oppenhemier-Volkoff 方程来进行的，同时考虑了相对论和有限温度效应。在 AdS 体中发现了新的“致密核心 - 稀释晕”密度分布，并在世界线形式主义中获得了相应的两点标量场相关器，作为对双场理论的探索。在这项工作中，我们涵盖了体积中费米子溶液的更广泛的自由参数空间（从稀到高度简并状态，包括引力坍缩的临界点），并通过计算正则势和自由熵来研究它们的热力学稳定性。这种稳定性分析是使用 Katz 判据进行的，这是一种历史上用于研究平坦空间中经典自引力系统的重力热灾难本身的技术。我们从体积和边界的角度确定了不稳定区域的一些特征，这些特征可以用作检测这种自引力系统不稳定性的代理。