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arXiv 0911.4574gr-qc
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关于霍金辐射的复路径分析

A note on Hawking radiation via complex path analysis

Sourav Bhattacharya

摘要:

只要我们忽略反向反应,一个给定的黑洞的霍金温度就不会依赖于我们所考虑的粒子种类的参数。在霍金辐射的半经典复路径分析方法中,这一点已经通过对不同的定态时空度规分别取标量旋量和狄拉克旋量得到了验证。在这里,我们表明,在一个坐标独立的方式,对于任意维数的任意时空,狄拉克旋量,矢量,自旋$2$和自旋$\frac{3}{2}$领域的运动方程减少到克莱因-戈登方程在WKB半经典极限。然后,我们得到,在一些适当的假设下,这些产生的标量方程的复杂的解决方案,通过一个固定的时空的Killing视界,得到一个坐标无关的表达式的发射概率相同的所有粒子物种。最后,我们考虑一些明确的例子来证明该表达式的有效性。

英文摘要:

As long as we neglect backreaction, the Hawking temperature of a given black hole would not depend upon the parameters of the particle species we are considering. In the semiclassical complex path analysis approach of Hawking radiation, this has been verified by taking scalar and Dirac spinors separately for different stationary spacetime metrics. Here we show, in a coordinate independent way that, for an arbitrary spacetime with any number of dimensions, the equations of motion for a Dirac spinor, a vector, spin-$2$ and spin-$\frac{3}{2}$ fields reduce to Klein-Gordon equations in the WKB semiclassical limit. We then obtain, under some suitable assumptions, the complex solutions of those resulting scalar equations across the Killing horizon of a stationary spacetime to get a coordinate independent expression for the emission probability identical for all particle species. Finally we consider some explicit examples to demonstrate the validity of that expression.

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