Massive scalar field perturbations in noncommutative-geometry-inspired Schwarzschild black hole

Abstract

In this paper, based on noncommutative-geometry-inspired Schwarzschild black hole, we employ a third-order WKB approximation approach to systematically calculate the quasinormal mode frequencies (QNFs), greybody factors (GFs), and absorption cross section (ACS) under massive scalar field perturbations. The results show that the QNFs satisfy Im($ω$)<0, confirming the stability of the black hole under perturbations. Furthermore, increasing the noncommutative parameter $θ$ reduces the absolute values of both the real and imaginary parts of the frequency, while increasing mass $μ$ increases the real part and reduces the imaginary part. The GFs and ACS increase with increasing $θ$ and decrease with increasing $μ$, indicating opposite modulation effects of these two types of parameters. It is worth emphasizing that the QNFs of the extreme black hole approach the corresponding values of the classical Schwarzschild black hole at angular quantum number $\ell=1$ and large $μ$, suggesting that, the effects of mass and noncommutative geometry quantum corrections cancel each other out to some extent. It is hoped that these results provide a viable theoretical basis for both the theoretical and experimental aspects of the perturbative dynamics of black hole.

Figures (8)

• Figure 1: (Color online) The metric function $f(r)$ versus $r$, for different values of $\xi \equiv M / \sqrt{\theta}$.
• Figure 2: (Color online) The effective potential $V(r)$ versus $r$ with different (a) angular quantum number $\ell$, (b) nonaommutative parameter $\theta$, and (c) scalar mass $\mu$.
• Figure 3: (Color online) The evolution of the real part $\mathrm{Re}(\omega)$ and the imaginary part $-\mathrm{Im}(\omega)$ of QNFs as a function of the noncommutative parameter $\theta$ for representative scalar mass.
• Figure 4: (Color online) The QNFs for different $\ell$ and $n$ at $\theta=0.0,~0.2758$. Circles denote $\theta = 0.2758$, and diamonds denote $\theta = 0.0$. Yellow, purple and cyan represent $\ell=1,2,3$, respectively. Points from top to bottom correspond to $n=0,1,2$ ($\mu=0.2$).
• Figure 5: (Color online) The evolution of the real and imaginary parts of the QNFs—$\mathrm{Re}(\omega)$ and $\mathrm{Im}(\omega)$—as a function of $\mu$ for classical Schwarzschild black hole $\theta=0.0$ and extreme black hole $\theta=0.2758$, the red dot indicates the critical point where $\omega^2 > \mu^2$.