透過廣義不確定性原理重新審視霍金輻射

Revisiting Hawking Radiation via Generalized Uncertainty Principle

周天朗(Tin-Long Chau)

指導教授 ： 賀培銘

國立臺灣大學/理學院/物理學系/碩士(2024年)

https://doi.org/10.6342/NTU202401546

摘要

量子引力理論中通常會出現一個基本的最小長度，一般被認為是普朗克長度或是弦的長度。為了進一步的探討，我們考慮了一種包含廣義不確定性原理的理論，並將其應用於重新審視霍金輻射。我們評估了維迪雅黑洞和自由落體座標中隨時間變化的霍金輻射振幅。雖然廣義不確定性原理對霍金溫度的修正只是微擾性的，但我們發現霍金輻射在擾亂時間(scrambling time)後被停止了。這一停止代表了黑洞晚期行為的重大改變，使人們對資訊悖論的標準解釋的可靠性產生了懷疑。

關鍵字

霍金輻射 ； 量子黑洞 ； 廣義不確定性原理 ； 霍金溫度 ； 資訊悖論

並列摘要

In quantum gravity theory, a fundamental minimum length, typically identified as the Planck length or the length of a string, commonly emerges. To explore this further, we consider a theory incorporating the generalized uncertainty principle (GUP) and apply this to Hawking radiation. We evaluate the time-dependent amplitude of Hawking radiation in both the Vaidya black hole and the freely falling frame. While the correction to the Hawking temperature is only perturbative, we find that the Hawking radiation is turned off around the scrambling time. This termination represents a significant modification in the late-time behavior of the black hole, which casts doubt on the reliability of the standard interpretation of the information loss paradox.

並列關鍵字

Hawking radiation ； quantum black hole ； generalized uncertainty principle ； Hawking temperature ； information loss paradox

參考文獻

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