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arXiv 0812.2600gr-qc
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Schwarzschild黑弦时空背景中幻影标量微扰的动力学演化

Dynamical evolution of phantom scalar perturbation in the background of Schwarzschild black String spacetime

Songbai Chen, Jiliang Jing

摘要:

利用Leaver连分式和时域方法,研究了Schwarzschild黑弦时空中虚标微扰的波动力学性质。我们发现准正规模包含了第五维波数$k$的印记。后期的行为是由波数$k$和质量$μ$的幻影标量扰动之间的差异。对于$k<μ$,在晚期演化中的幻影标量扰动与四维史瓦西黑洞时空一样以指数速率增长。而对于$k=μ$,其后期行为与黑洞背景中无质量标量场扰动的形式相同.此外,对于$k>μ$,幻影标量扰动的后期演化是由一个衰减的尾巴与振荡,这是一致的,通常的大质量标量场。因此,史瓦西黑弦只有在满足波长$λ>2π/μ$的幻象标量扰动下才是不稳定的。这些信息有助于我们进一步了解虚标微扰的波动力学和黑弦的性质。

英文摘要:

Using Leaver's continue fraction and time domain method, we study the wave dynamics of phantom scalar perturbation in a Schwarzschild black string spacetime. We find that the quasinormal modes contain the imprint from the wavenumber $k$ of the fifth dimension. The late-time behaviors are dominated by the difference between the wavenumber $k$ and the mass $μ$ of the phantom scalar perturbation. For $k<μ$, the phantom scalar perturbation in the late-time evolution grows with an exponential rate as in the four-dimensional Schwarzschild black hole spacetime. While, for $k=μ$, the late-time behavior has the same form as that of the massless scalar field perturbation in the background of a black hole. Furthermore, for $k>μ$, the late-time evolution of phantom scalar perturbation is dominated by a decaying tail with an oscillation which is consistent with that of the usual massive scalar field. Thus, the Schwarzschild black string is unstable only against the phantom scalar perturbations which satisfy the wavelength $λ>2π/μ$. These information can help us know more about the wave dynamics of phantom scalar perturbation and the properties of black string.

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