Anisotropic radiation field and trapped photons around the Kerr black hole
Anisotropic radiation field and trapped photons around the Kerr black hole
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DOI：
10.1051/0004-6361/200913534
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发表时间：
2010-02
影响因子：
6.5
通讯作者：
R. Takahashi;M. Takahashi
中科院分区：
文献类型：
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作者：
R. Takahashi;M. Takahashi
目标。为了了解旋转黑洞周围弯曲时空中局部辐射场的各向异性特性，我们研究了位于黑洞附近的观察者所看到的黑洞的出现。当黑洞位于光源前面时，黑洞会在照明中投射阴影。因此，黑洞的出现被称为黑洞阴影。方法：研究方法。我们首先用观察者在局部非旋转参考系(LNRF)中看到的光子的运动常数来解析地描述阴影的形状。然后，我们重新推导了阴影立体角的实用方程。在第三步中，我们可以很容易地绘制出黑洞阴影的表观图像。最后，我们还计算了黑洞附近发射的光子被黑洞捕获的光子和逃逸光子与远处区域的比率。结果。从黑洞阴影的形状和大小，我们可以理解弯曲时空的特征，即黑洞的质量和自转。我们的阴影立体角公式在计算光子俘获比方面具有技术优势。也就是说，这个方程在计算上非常容易，并且给出了非常精确的结果。这是因为这个方程是用单参数积分来描述的，其中考虑了黑洞的自旋和位置的给定值。此后，无需对光子的零测地线进行数值计算，即可得到立体角。
Aims. In order to understand the anisotropic properties of local radiation field in the curved spacetime around a rotating black hole, we investigate the appearance of a black hole seen by an observer located near the black hole. When the black hole is in front of a source of illumination the black hole casts shadow in the illumination. Accordingly, the appearance of the black hole is called the black hole shadow. Methods. We first analytically describe the shape of the shadow in terms of constants of motion for a photon seen by the observer in the locally non-rotating reference frame (LNRF). Then, we newly derive the useful equation for the solid angle of the shadow. In a third step, we can easily plot the apparent image of the black hole shadow. Finally, we also calculate the ratio of the photon trapped by the hole and the escape photon to the distant region for photons emitted near the black hole. Results. From the shape and the size of the black hole shadow, we can understand the signatures of the curved spacetime; i.e., the mass and spin of the black hole. Our equations for the solid angle of the shadow has technical advantages in calculating the photon trapping ratio. That is, this equation is computationally very easy, and gives extremely precise results. This is because this equation is described by the one-parameter integration with given values of the spin and location for the black hole considered. After this, the solid angle can be obtained without numerical calculations of the null geodesics for photons.