5维黑弦时空中标量场辐射的数值解

The Numerical Solution of Scalar Field in 5D SdS Black String Space

使用无质量的标量粒子作为检验粒子,研究它在5D黑弦背景时空中的运动以及额外第五维对Hawking辐射的影响.经过乌龟坐标变换后,径向方程变成一个类Schrdinger形式的主方程.在求解粒子的径向运动之前,我们针对Nariai黑洞的极端情况来确定参数,然后确定边界条件并采用了多项式近似,最后利用数学软件求得了粒子径向运动的数值解.从最终的结果来看,粒子在视界之间的波形近似谐波,并且在接近视界处波形迅速堆积起来.

In this paper we take the massless scalar particles as test particles to study its movement in the 5D black string space background and the influence of the fifth dimension to the radiation. The radial equation turns to a Schodingerlike master equation after tortoise coordinate alternation. Before solving the master equation, we adopt the Nariai case to determine the parameter and ascertain the boundary conditions. Then under the polynomial approximation, the numerical solution of the radial equation is obtained through mathmatica software. The ultimate result shows that the wayc is similar to harmonic one between the horizons and piles up rapidly near the horizons. Furthermore, the approximate synchronous accumulation near the two horizons shows that their traits are homologous.