Gauss-Bonnet 重力理論中穿隧效應的霍金輻射

Hawking Radiation as Tunneling in Gauss-Bonnet Gravity

黃英明(Ying-Ming Huang)

指導教授 ： 陳江梅

國立中央大學/理學院/物理學系/碩士(2007年)

摘要

在1974年，霍金率先提出在古典黑洞彎曲時空下場論的量子化效應會導致黑洞有熱輻射現象。經過了 30幾年之後，在1999年Wilzcek 和他的學生Parikh 提出一個非常漂亮的方法來處理霍金熱輻射。他們的方法是把球對稱黑洞視界附近霍金輻射當成是一種半古典的穿隧過程。這種穿隧過程隱含了動態黑洞幾何。我們將Parikh 和Wilzcek的方法應用到Gauss-Bonnet 黑洞上。Gauss-Bonnet 重力理論中廣義的黑洞可具有三種不同的空間曲率：k = 1為球形式，k = -1為馬鞍形，k = 0為平直形。我們經由穿隧效應的方法去計算這三類型式黑洞的熵，結果和從熱力學第一定律所獲得的熵是相等的。我們驗證了Parikh-Wilzcek的穿隧效應計算霍金輻射的方法也適用於Gauss-Bonnet理論的黑洞。

關鍵字

穿隧效應 ； 熵 ； 空間曲率 ； 霍金輻射

並列摘要

In 1974 Hawking had proposed the idea of the emission of thermal radiation from a black hole under the field theory quantized on classical curved spacetime. In 1999 Parikh and Wilzcek proposed an elegant method to treat the Hawking radiation as a semi-classical tunneling process near the event horizon of a spherically symmetric black hole. Their method incorporates the effects of a dynamical black hole geometry. We apply Parikh and Wilzcek’s method to Gauss-Bonnet black holes. We consider three types of “generalized black hole” with different spatial curvature, namely k = 1 for spherical, k = −1 for hyperbolic and k = 0 for flat, in Gauss-Bonnet gravity. We discover that the entropy obtained from the tunneling approach is consistent with the result derived from the first law calculation. Therefore, we show that the
tunneling approach works for the Gauss-Bonnet black holes with zero curvature, negative constant curvature and positive constant curvature hypersurfaces.

並列關鍵字

Hawking radiation ； entropy ； curvature ； tunneling

參考文獻

[2] R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics”, Phys. Rev. Lett. 11, 237 (1963).

[3] F. R. Tangherlini, “Schwarzschild field in N dimensions and the dimensionality of space problem”, Nuovo Cim. 27, 636 (1963).

[5] B. Carter, “Hamilton-Jacobi and Schr¨odinger separable solutions of Einstein’s equations”, Commun. Math. Phys. 10, 280 (1968).

[7] G. W. Gibbons, H. Lu, D. N. Page and C. N. Pope, “The general Kerr-de Sitter metrics in all dimensions”, J. Geom. Phys. 53, 49-73 (2005).

[8] D. G. Boulware and S. Deser, “String-generated gravity models”, Phys. Rev.Lett. 55, 2656 (1985).