论文标题
标量场的准模式与非交通几何形状启发的黑洞中的爱因斯坦的张量
Quasinormal modes of scalar field coupled to Einstein's tensor in the non-commutative geometry inspired black hole
论文作者
论文摘要
我们研究了标量场的准模式（QNM），该模式与爱因斯坦的张量相结合，在非共同的几何形状灵感启发的黑洞时空中。发现非交通黑洞度量的失误函数可以用Kummer的汇合高几何函数表示，这可以有效地解决QNM的数值结果对模型参数敏感并使QNMS值更可靠的问题。我们通过使用几种数值方法对标量QNM频率进行仔细分析，并发现通过新的WKB方法获得的数值结果（padé近似值）和mashhoon方法（p $ \ ddot {\ ddot {\ text {o}} $ schl-teller潜在方法与那些获得的方法（通过那些获得的方法）（Aimitative and Antimation-Atime and abletiation-Atime and-Atimitiation-Atime） - 目的 - 非交换参数$θ$和耦合参数$η$很大。最明显的区别在于，通过目标获得的数值结果和时域集成方法似乎是关键值$η_c$，并增加了$η$，从而导致动态不稳定性。在仔细分析了数字结果之后，我们得出结论，与WKB方法和Mashhoon方法相比，通过目标获得的数值和时域积分方法更接近理论值。此外，通过数值拟合，我们获得了阈值$η_c$与非交易参数$θ$之间的功能关系满足固定$ l $的$η_{c} =aθ^{b}+c $。我们发现可以在$η<η_c（θ，l）$区域中确保动力学的稳定性。
We investigate the quasinormal modes (QNMs) of the scalar field coupled to the Einstein's tensor in the non-commutative geometry inspired black hole spacetime. It is found that the lapse function of the non-commutative black hole metric can be represented by a Kummer's confluent hypergeometric function, which can effectively solve the problem that the numerical results of the QNMs are sensitive to the model parameters and make the QNMs values more reliable. We make a careful analysis of the scalar QNM frequencies by using several numerical methods, and find that the numerical results obtained by the new WKB method (the Padé approximants) and the Mashhoon method (P$\ddot{\text{o}}$schl-Teller potential method) are quite different from those obtained by the asymptotic iterative method (AIM) and time-domain integration method when the non-commutative parameter $θ$ and coupling parameter $η$ are large. The most obvious difference is that the numerical results obtained by the AIM and the time-domain integration method appear a critical value $η_c$ with an increase of $η$, which leads to the dynamical instability. After carefully analyzing the numeral results, we conclude that the numerical results obtained by the AIM and the time-domain integration method are closer to the theoretical values than those obtained by the WKB method and the Mashhoon method, when the $θ$ and $η$ are large. Moreover, through a numerical fitting, we obtain that the functional relationship between the threshold $η_c$ and the non-commutative parameter $θ$ satisfies $η_{c}=aθ^{b}+c$ for a fixed $l$ approximately. We find that the stability of dynamics can be ensured in the $η<η_c(θ, l)$ region.
