论文标题
Kerr-Newman黑洞周围的球形光子轨道半径
Radii of spherical photon orbits around Kerr-Newman black holes
论文作者
论文摘要
黑洞周围的球形光子轨道在黑洞的天体物理观察中特别重要。在本文中，研究了Kerr-Newman黑洞周围的赤道和非赤道球形光子轨道。这些轨道的半径可满足带有三个参数的六元多项式方程，旋转参数$ u $，电荷参数$ w $和有效的倾斜角$ v $。发现有两个极性轨道，一个在内部，另一个在事件范围之外。对于赤道平面中极端Kerr-Newman黑洞的轨道，我们找到了方程式的三种正解，并为三个轨道的半径提供了分析公式。还发现，旋转参数的临界值$ u = \ frac {1} {4} $在上面存在，在事件范围之外只有一个逆行轨道，在事件范围之外存在两个轨道（一个旋转和一个逆行）。对于非Xtremal Kerr-Newman黑洞赤道平面中的轨道，有四个或两个正溶液。还发现了分开区域的$（u，w）$ - 平面的关键曲线。在此临界曲线上，发现了三种溶液的明确公式。在这种情况下，事件范围之外总是存在两个赤道光子轨道。对于上述两个特殊平面之间的轨道，有四个或两种通用六式方程的解决方案。当黑洞是极端的时，发现存在一个关键的倾斜角$ v_ {cr} $，在此下，只有一个轨道存在，高于该轨道，而在事件范围之外存在两个轨道，用于快速旋转的黑洞$ u> \ frac {1} {1} {4} $。在这个临界倾斜角度，也得出了半径的精确公式。最后，显示了（$ u，w，v $）参数空间中的临界表面，该表面用四个或两个解决方案将区域分开。
The spherical photon orbits around a black hole with constant radii are particular important in astrophysical observations of the black hole. In this paper, the equatorial and non-equatorial spherical photon orbits around Kerr-Newman black holes are studied. The radii of these orbits satisfy a sextic polynomial equation with three parameters, the rotation parameter $u$, charge parameter $w$ and effective inclination angle $v$. It is found that there are two polar orbits and one is inside and the other is outside the event horizon. For orbits in the equatorial plane around an extremal Kerr-Newman black hole , we find three positive solutions to the equation and provide analytical formulas for the radii of the three orbits. It is also found that a critical value of rotation parameter $u=\frac{1}{4}$ exists, above which only one retrograde orbit exists outside the event horizon and below which two orbits (one prograde and one retrograde) exist outside the event horizon. For orbits in the equatorial plane of a nonextremal Kerr-Newman black hole, there are four or two positive solutions. A critical curve in $(u,w)$-plane which separates the regions is also found. On this critical curve, the explicit formulas of three solutions are found. There always exist two equatorial photon orbits outside the event horizon in this case. For orbits between the above two special planes, there are four or two solutions to the general sextic equation. When the black hole is extremal, it is found that there is a critical inclination angle $v_{cr}$, below which only one orbit exists and above which two orbits exist outside the event horizon for a rapidly rotating black hole $u>\frac{1}{4}$. At this critical inclination angle, exact formula for the radii is also derived. Finally, a critical surface in parameter space of ($u,w,v$) is shown that separates regions with four or two solutions.
