Rainbow scattering of gravitational plane waves by a compact body
Rainbow scattering of gravitational plane waves by a compact body
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DOI：
10.1103/physrevd.100.024007
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发表时间：
2019-02
影响因子：
5
通讯作者：
Tom Stratton;S. Dolan
中科院分区：
文献类型：
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作者：
Tom Stratton;S. Dolan
本文研究了平面引力波在紧致弯曲时空中的散射问题。我们开始考虑的几何光学极限，其中的引力波传播沿着零测地线的时空，我们表明，波前通过一个中子星星的稀薄R/M=6将集中在一个尖焦散附近的星星的表面。其次，利用球对称时空上的线性化爱因斯坦场方程，我们构造了奇偶校验扇区中的度规扰动;并且，利用分波方法，我们数值计算了螺旋度守恒和螺旋度反转振幅的引力散射截面。在长波长下，横截面对恒星结构不敏感，在极限Mω→0时，它简化为已知的黑洞情况的低频近似。在更高的频率Mω <$1，引力波探测物体的内部结构。从本质上讲，我们发现引力波的横截面与无质量标量场的横截面相似，尽管存在着由非零螺旋反转振幅以及引力波与物体流体之间偶宇称扇区的耦合引起的微妙影响。该横截面具有叠加在卢瑟福横截面上的Airy型振荡的彩虹散射。我们表明，彩虹角，这是从一个固定的点在测地线偏转功能，依赖于多方指数。原则上，彩虹散射提供了致密天体状态方程的诊断;但是，在实践中，这需要一个高频率的引力波天体物理源。
We study the time-independent scattering of a planar gravitational wave propagating in the curved spacetime of a compact body with a polytropic equation of state. We begin by considering the geometric-optics limit, in which the gravitational wave propagates along null geodesics of the spacetime; we show that a wavefront passing through a neutron star of tenuity R/M=6 will be focused at a cusp caustic near the star’s surface. Next, using the linearized Einstein field equations on a spherically symmetric spacetime, we construct the metric perturbations in the odd and even parity sectors; and, with partial-wave methods, we numerically compute the gravitational scattering cross section from helicity-conserving and helicity-reversing amplitudes. At long wavelengths, the cross section is insensitive to stellar structure and, in the limit Mω→0, it reduces to the known low-frequency approximation of the black hole case. At higher frequencies Mω≳1, the gravitational wave probes the internal structure of the body. In essence, we find that the gravitational wave cross section is similar to that for a massless scalar field, although with subtle effects arising from the nonzero helicity-reversing amplitude, and the coupling in the even-parity sector between the gravitational wave and the fluid of the body. The cross section exhibits rainbow scattering with an Airy-type oscillation superposed on a Rutherford cross section. We show that the rainbow angle, which arises from a stationary point in the geodesic deflection function, depends on the polytropic index. In principle, rainbow scattering provides a diagnostic of the equation of state of the compact body; but, in practice, this requires a high-frequency astrophysical source of gravitational waves.