The Correction of Quantum Tunneling Rate and Entropy of Non-Stationary Spherically Symmetric Black Hole by Lorentz Breaking

Round 1

Reviewer 1 Report

Referee report Universe 010623

Yu-Zhen Liu, Xia Tan, Jie Zhang, Ran Li and Shu-Zheng Yang

The correction of quantum tunneling rate and entropy of non-stationary spherically symmetric black hole by Lorentz breaking

This is a well written research article with interesting new results. The language is reasonably good.  In my opinion the paper can be published in Universe without any changes.

Author Response

Thanks for your comment and recognition！ wishing you all the best！

Reviewer 2 Report

The authors of this paper have carried out an interesting exploration of the Lorentz-breaking theory, WKB approximation, and quantum tunneling radiation theory, focusing on the modified fermion dynamics equation in non-stationary spherically symmetric black hole space-time. The derived new modified expressions for the fermion tunneling rate, the Hawking temperature, and the Bekenstein-Hawking entropy provide compelling insights.

1. The paper demonstrates a comprehensive understanding of Lorentz-breaking theory and its applications in the study of fermion dynamics in curved space-time.

2. The derived equations for the Hawking temperature and the energy level distribution of the Vaidya-Bomer black hole after correction are noteworthy contributions.

3. The authors' examination of the impact of the CFJ term, aether-like field term, and Charial term in the context of Lorentz breaking, and the resulting implications for the quantum tunneling rate and entropy of different black holes, are significant additions to the body of knowledge in this field.

Minor Revisions Required:

1. The abstract could be further expanded upon, with a more detailed background introduction, an explanation of the research significance, and a clearer delineation of the main research outcomes.

2. While the paper's conclusion discusses the effects of the chiral term, aether-like term, and CFJ term on the energy level distribution of the Dirac particle, it would benefit from more detailed elaboration and interpretation of these results.

3. The paper could be improved by providing more context and explanation for the specific findings. For instance, it is stated that the correction of quantum tunneling rate and the correction of entropy of different black holes vary, but the reasons for these variations are not explored.

4. The authors should compare their findings with previous studies on quantum tunneling and Hawking radiaiton. This would help establish the novelty and significance of their results. If there are any discrepancies or agreements with existing literature, they should be discussed in detail. For example, there are several works in the literature such as hep-th/0608098,  0804.2289, 1810.09322, 1707.00169.

 

1.  The conclusions section states that "specific conclusions need to be analyzed." It would be beneficial if the authors were to delve deeper into these analyses within the paper itself.

Overall, this paper offers an new perspective on the study of fermion dynamics in curved space-time under the Lorentz breaking theory. However, the authors need to make minor revisions to provide more depth and context to their findings, enhancing the overall clarity and value of the research. Once these are addressed, the paper should make a strong contribution to the field.

Author Response

1.As requested, we have added some content.

2.In the discussion, we explained the impact of three correction terms on the research results.

3.We provide an explanation of the results obtained in the article and explain the significance of their application.  Add content for analysis and discussion.

4.Our focus is on the impact of three correction terms on the study of non-statinary spherically symmetric black holes and our study is based on the articles you provideed.

Thanks for your work！ wishing you all the best！

Reviewer 3 Report

In this article, Lorentz symmetry breaking is considered to find corrections to the quantum tunnelling rate and entropy of black holes. The modified fermion dynamics equation is studied in the general non-stationary spherically symmetric black hole space-time, and new modified expressions of the fermion tunnelling rate, Hawking temperature, and Bekenstein-Hawking entropy of the black hole are obtained using the WKB approximation.

This research provides a new perspective on the behavior of black holes by incorporating Lorentz breaking. The corrected expressions for the tunnelling rate, Hawking temperature, and Bekenstein-Hawking entropy of black holes can help us better understand the thermodynamic properties of black holes and their evolution over time. I ask the authors to address the following points before further considering the article for publication in the Universe.

1.     In the introduction, it should be that “gravity cannot be renormalized”  and “Grand Unified Theory”.

2.     The conjugate of Dirac equation in Eq. 6 and Eq. 12 are incorrect. Please check.

3.     Inverse metric tensor in Eq. 27 should have g^{00} component.

4.     Authors should interpretate their results; how does the Lorentz symmetry breaking changes the black hole thermodynamical features.

 

 

Moderate editing of English language required. Correct the typos such as "characterist0ics" on page no. 2.

Author Response

1.The text content has been modified according to your requirements.

2. Equations （6） and （12） are changed.

3.For g⁰⁰=0, we added explanation in the article.

4.In this paper, we add the relevant content about the influence of Lorentz breaking on black hole thermodynamics. The quality of English has been checked.

Thanks for your work！ wishing you all the best！

Round 2

Reviewer 3 Report

The authors have satisfactorily addressed my queries. I recommend the article for publication in the Universe.