Abstract

We study the nature of phase transitions between gaseous and condensed states in the self-gravitating Fermi gas at finite temperature in general relativity. The condensed states can represent compact objects such as white dwarfs, neutron stars, or dark matter fermion balls. The caloric curves depend on two parameters: the system size R and the particle number N. When N < N_OV, where N_OV is the Oppenheimer–Volkoff limit, there exists an equilibrium state for any value of the temperature T and energy E as in the nonrelativistic case [P.H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006)]. Gravitational collapse is prevented by quantum mechanics (Pauli’s exclusion principle). When N > N_OV, there is no equilibrium state below a critical energy and below a critical temperature. In that case, the system is expected to collapse toward a black hole. We plot the caloric curves of the general relativistic Fermi gas, study the different types of phase transitions that occur in the system, and determine the phase diagram in the (R, N) plane. The nonrelativistic results are recovered for N ≪ N_OV and R ≫ R_OV with N^R3 fixed. The classical (non quantum) results are recovered for N ≫ N_OV and R ≫ R_OV with N∕R fixed. We discuss the commutation of the limits c → +∞ and ℏ → 0. We study the relativistic corrections to the nonrelativistic caloric curves and the quantum corrections to the classical caloric curves. We highlight a situation of physical interest where a self-gravitating Fermi gas, by cooling, first undergoes a phase transition toward a compact object (white dwarf, neutron star, dark matter fermion ball), then collapses into a black hole. This situation occurs in the microcanonical ensemble when N_OV < N < 3.73 N_OV. We also relate the phase transitions from a gaseous state to a core-halo state in the microcanonical ensemble to the onset of red-giant structure and to the supernova phenomenon.

Graphical abstract

中文翻译：

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广义相对论中自重费米子的热量曲线

摘要

我们以广义相对论研究了自重费米气体在有限温度下的气态和冷凝态之间的相变性质。凝聚态可以表示紧凑的物体，例如白矮星，中子星或暗物质费米子球。热量曲线取决于两个参数：系统尺寸ř和粒子数Ñ。当N < N _OV，其中N _OV是Oppenheimer-Volkoff极限时，对于温度T和能量E的任何值都存在一个平衡状态，如在非相对论情况下[PH Chavanis，Int。J.莫德 物理 B 20，3113（2006）]。量子力学可以防止引力坍塌（保利的排除原理）。当N > N _OV时，在临界能量以下和临界温度以下没有平衡状态。在这种情况下，系统可能会朝黑洞崩溃。我们绘制了广义相对论费米气体的热量曲线，研究了系统中发生的不同类型的相变，并确定了（R，N）平面中的相图。非相对论结果回收Ñ « Ñ _OV和- [R » ř _OV与ñ ^{- [R 3}固定。经典的（非量子）结果回收用于Ñ » Ñ _OV和- [R » ř _OV与ñ / [R固定。我们讨论极限c →+ ∞和ℏ的交换→0。我们研究非相对论热曲线的相对论校正和经典热曲线的量子校正。我们重点介绍了一种物理关注的情况，即自重力费米气体通过冷却首先经历向着紧凑物体（白矮星，中子星，暗物质费米子球）的相变，然后坍塌成黑洞。当N _OV < N <3.73 N _OV时，这种情况就会在微典范合奏中发生。我们还将微规范集合中从气态到核-卤态的相变与红巨人结构的出现和超新星现象相关。

图形概要