In this note we explore a non-static spacetime in quantum regime in the background of f ( R ) gravity. The time dependent Vaidya metric which represents the spacetime of a radiating body like star is studied in an energy dependent gravity's rainbow, which is a UV completion of General Relativity. In our quest we have used gravitational collapse as the main tool. The focus is to probe the nature of singularity (black hole or naked singularity) formed out of the collapsing procedure. This is achieved via a geodesic study. For our investigation we have considered two different models of f ( R ) gravity, namely the inflationary Starobinsky's model and the power law model. Our study reveals the fact that naked singularity is as good a possibility as black hole as far as the central singularity is concerned. Via a proper fine tuning of the initial data, we may realize both black hole or naked singularity as the end state of the collapse. Thus this study is extremely important and relevant in the light of the Cosmic Censorship hypothesis. The most important result derived from the study is that gravity's rainbow increases the tendency of formation of naked singularities. We have also deduced the conditions under which the singularity will be a strong or weak curvature singularity. Finally in our quest to know more about the model we have performed a thermodynamical study. Throughout the study we have obtained results which involve deviation from the classical set-up. Such deviations are expected in a quantum evolution and can be attributed to the quantum fluctuations that our model suffers from. It is expected that this study will enhance our knowledge about quantization of gravity and subsequently about the illusive theory of quantum gravity.

中文翻译：

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f(R) 引力中的非静态量子启发时空：引力彩虹。

在这篇文章中，我们探索了 f ( R ) 引力背景下量子体系中的非静态时空。与时间相关的 Vaidya 度量代表了像恒星这样的辐射体的时空，在与能量相关的引力彩虹中进行了研究，这是广义相对论的 UV 完成。在我们的探索中，我们使用引力塌缩作为主要工具。重点是探索坍缩过程中形成的奇点（黑洞或裸奇点）的本质。这是通过测地线研究实现的。在我们的研究中，我们考虑了 f ( R ) 引力的两种不同模型，即暴胀 Starobinsky 模型和幂律模型。我们的研究揭示了这样一个事实：就中心奇点而言，裸奇点的可能性与黑洞一样好。通过对初始数据进行适当的微调，我们可以认识到黑洞或裸奇点都是坍缩的最终状态。因此，根据宇宙审查假说，这项研究极其重要且相关。这项研究最重要的结果是，引力彩虹增加了裸奇点形成的趋势。我们还推导了奇点为强曲率奇点或弱曲率奇点的条件。最后，为了更多地了解该模型，我们进行了热力学研究。在整个研究过程中，我们获得的结果与经典设置存在偏差。这种偏差在量子演化中是预料之中的，并且可以归因于我们的模型所遭受的量子涨落。预计这项研究将增强我们对引力量子化以及随后对虚幻的量子引力理论的了解。