Abstract

We study the power spectrum of the uniformly accelerating scalar field, obeying the \(\kappa \) -deformed Klein–Gordon equation. From this we obtain the \(\kappa \) -deformed corrections to the Unruh temperature, valid up to first order in the \(\kappa \) -deformation parameter a. We also show that in the small acceleration limit, this expression for the Unruh temperature in \(\kappa \) -deformed space-time is in exact agreement with the one derived from the \(\kappa \) -deformed uncertainty relation. Finally, we obtain an upper bound on the deformation parameter a.

中文翻译：

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$$\kappa $$ -变形功率谱和修改的Unruh温度

摘要

我们研究均匀加速标量场的功率谱，遵循\(\kappa \)变形的克莱因-戈登方程。由此，我们获得了对 Unruh 温度的 \(\kappa \)变形校正，在\(\kappa \)变形参数a中对一阶有效。我们还表明，在小加速度极限下，\(\kappa \)变形时空中的 Unruh 温度表达式与从\(\kappa \)变形不确定性关系导出的表达式完全一致。最后，我们获得变形参数a的上限。