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arXiv 2201.00066hep-thgr-qc
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弯曲时空中无质量粒子的热力学

Thermodynamics of massless particles in curved spacetime

A. A. Araújo Filho

AI总结:

本文在Einstein-aether形式体系中研究弯曲时空下无质量粒子的热力学,通过正则系综推导了各热力学量及对Stefan-Boltzmann定律的修正,并解析与数值分析了宇宙三个温度阶段下的结果。

摘要:

本工作致力于研究弯曲时空背景下无质量粒子的行为。本质上,我们在Einstein-aether(爱因斯坦-以太)形式体系中研究了Friedmann-Robertson-Walker度规的标度因子$C(η)$的后果,以研究类光子粒子。为此,我们在正则系综形式体系中考虑该系统,以推导以下热力学状态量:光谱辐射度、Helmholtz自由能、压强、熵、平均能量和热容。此外,还提供了对Stefan-Boltzmann定律和状态方程的修正。特别地,我们将研究分为三种不同情况,即$s=0,p=0$;$s=1,p=1$;$s=2,p=1$。在第一种情况中,结果通过数值方法导出。然而,对于其余情况,所有计算均以解析方式完成,明确展示了标度因子$C(η)$和Riemann zeta函数$ξ(s)$的依赖关系。此外,我们的分析总体上考虑了宇宙温度的三个不同阶段,即暴胀时期($T=10^{13}$ GeV)、电弱时期($T=10^{3}$ GeV)和宇宙微波背景($T=10^{-13}$ GeV)。

英文摘要:

This work is devoted to study the behavior of massless particles within the context of curved spacetime. In essence, we investigate the consequences of the scale factor $C(η)$ of the Friedmann-Robertson-Walker metric in the Einstein-aether formalism to study photon-like particles. To do so, we consider the system within the canonical ensemble formalism in order to derive the following thermodynamic state quantities: spectral radiance, Helmholtz free energy, pressure, entropy, mean energy and the heat capacity. Moreover, the correction to the Stefan-Boltzmann law and the equation of states are also provide. Particularly, we separate our study within three distinct cases, i.e., $s=0,p=0$; $s=1,p=1$; $s=2,p=1$. In the first one, the results are derived numerically. Nevertheless, for the rest of the cases, all the calculations are accomplished analytically showing explicitly the dependence of the scale factor $C(η)$ and the Riemann zeta function $ξ(s)$. Furthermore, our analyses are accomplished in general taking into account three different regimes of temperature of the universe, i.e., the inflationary era ($T=10^{13}$ GeV), the electroweak epoch ($T=10^{3}$ GeV) and the cosmic microwave background ($T=10^{-13}$ GeV).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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