论文标题
弯曲时空中无质量颗粒的热力学
Thermodynamics of massless particles in curved spacetime
论文作者
论文摘要
这项工作致力于研究弯曲时空背景下无质量颗粒的行为。从本质上讲，我们研究了爱因斯坦 - 区域形式主义中弗里德曼·罗伯逊 - 沃克指标的比例因子$ c（η）的后果，以研究光子样粒子。为此，我们考虑了规范集成形式主义中的系统，以得出以下热力学状态数量：光谱辐射，Helmholtz自由能，压力，熵，平均能量和热容量。此外，还提供了对Stefan-Boltzmann法律和国家方程的纠正。特别是，我们在三种不同的情况下分开研究，即$ s = 0，p = 0 $; $ s = 1，p = 1 $; $ s = 2，p = 1 $。在第一个中，结果是在数值上得出的。然而，在其余情况下，所有计算都在分析上完成，明确显示了比例因子$ c（η）$和riemann zeta函数$ξ（s）$的依赖性。此外，我们的分析通常考虑到宇宙温度的三种不同的机制，即通货膨胀时代（$ t = 10^{13} $ gev），electroweak epoch（$ t = 10^{3} $ gev）和cosmic microwave（$ t = 10^{$ t = 10^{-13} $ gev）。
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).
