Physics Maths Engineering
The Effect of Rényi Entropy on Hawking Radiation
rnfinity
Yang Liu
Related Subjects
Abstract
It is widely believed that Hawking radiation originates from excitations near the horizons of black holes [1,2,3]. However, Giddings [2] proposed that the Hawking radiation spectrum that characterizes evaporating semi-classical black holes originates from a quantum “atmosphere”, which extends beyond the horizon of a black hole. Although several research projects have been conducted in this field, they have not yet taken into account the effect of Rényi entropy. In the present article, we will therefore consider the effect of Rényi entropy on Hawking radiation power. We assume that if the effect of Rényi entropy is very small, we suggest that the Hawking radiation should originate from the quantum “atmosphere” which extends beyond the black hole’s horizon for finite dimensions. That is, that Giddings’ suggestion is the more likely of the above possibilities. However, for infinite dimensions, both suggestions are equally credible. We briefly consider the very large effect of Rényi entropy on Hawking radiation power as well. We find that if the effect of Rényi entropy is very large and ω/TBH is very small, then the power spectral density SR is proportional to the power spectral density SBH.
Key Questions
What is the focus of the study?
This study investigates the impact of Rényi entropy on Hawking radiation, a crucial concept in black hole thermodynamics. The authors explore how modifying the entropy measure can affect the radiation emitted by black holes, providing new insights into the nature of quantum gravity and black hole dynamics.
What is Hawking radiation?
Hawking radiation refers to the theoretical radiation emitted by black holes due to quantum effects near the event horizon. It is a fundamental concept in theoretical physics, demonstrating how quantum mechanics and general relativity interact in the presence of extreme gravitational fields.
What is Rényi entropy?
Rényi entropy is a generalization of the Shannon entropy that measures the uncertainty or information content of a system. In the context of black holes, it provides an alternative way to quantify the entropy associated with the black hole's quantum state, which plays a key role in understanding the thermodynamics of black holes.
How does Rényi entropy affect Hawking radiation?
The study demonstrates that using Rényi entropy instead of the traditional Bekenstein-Hawking entropy leads to modifications in the emission rate of Hawking radiation. These modifications have potential implications for the study of black hole thermodynamics and could provide new insights into the behavior of black holes at the quantum level.
What are the key findings of the study?
The authors show that the incorporation of Rényi entropy modifies the Hawking radiation spectrum. The study suggests that this modification could provide a more nuanced understanding of black hole entropy and radiation, potentially offering new paths to resolving puzzles in quantum gravity and black hole information paradoxes.
What is the significance of this study in the field of black hole thermodynamics?
This study contributes to the ongoing efforts to understand the quantum aspects of black holes. By exploring the effect of Rényi entropy on Hawking radiation, it provides a new perspective on black hole entropy, which is crucial for understanding the ultimate fate of information inside black holes and the nature of quantum gravitational systems.
What are the implications for future research in quantum gravity?
The results of this study suggest that alternative entropy measures, such as Rényi entropy, may offer valuable insights into the quantum properties of black holes. Future research could explore how these modifications impact the information paradox, the stability of black holes, and the integration of quantum mechanics with general relativity in extreme conditions.
