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Shadows around the q-metric
Classical and Quantum Gravity ( IF 3.6 ) Pub Date : 2020-12-10 , DOI: 10.1088/1361-6382/abc223
J A Arrieta-Villamizar 1 , J M Velsquez-Cadavid 1 , O M Pimentel 1 , F D Lora-Clavijo 1 , A C Gutirrez-Pieres 1, 2
Affiliation  

One crucial problem in relativistic astrophysics is that of the nature of black hole candidates. It is usually assumed that astrophysical black holes are described by the Schwarzschild or Kerr space-times; however, there is no direct evidence to assert this. Moreover, there are various solutions in general relativity that can be alternatives to black holes, usually called black hole mimickers. In this work, we study the shadow produced by a compact object described by the q-metric, which is the simplest static and axially symmetric solution of Einstein equations with a non-vanishing quadrupole moment. This particular spacetime has the property of containing an independent parameter $q$, which is related to the compact object deformation. The solution corresponds to naked singularities for some specific values of this parameter. Additionally, we analyze the eigenvalues of the Riemann tensor using the $SO(3,C)$ representation, which allows us to find, in an invariant way, regions where there may be repulsive effects. Furthermore, we numerically solve the motion equations to show the shadow, the Einstein ring, and the gravitational lensing to establish a possible signature of such repulsive effects. We found that as $q$ is smaller, the Einstein ring decreases, but the shape is the same as the Schwarzschild black hole case. However, for values of $q$ lower or equal than $-0.5$, repulsive gravitational effects appear in the gravitational lensing close to the compact object, where a strong dependence of the system to the initial conditions seems to take place.

中文翻译:

q-metric 周围的阴影

相对论天体物理学中的一个关键问题是黑洞候选者的性质。通常假设天体物理黑洞是由 Schwarzschild 或 Kerr 时空描述的;然而,没有直接证据可以断言这一点。此外,广义相对论中有各种解决方案可以替代黑洞,通常称为黑洞模仿者。在这项工作中,我们研究了由 q-metric 描述的紧凑物体产生的阴影,q-metric 是具有非零四极矩的爱因斯坦方程的最简单的静态和轴对称解。这个特定的时空具有包含独立参数 $q$ 的属性,该参数与紧凑物体变形有关。该解对应于该参数的某些特定值的裸奇点。此外,我们使用 $SO(3,C)$ 表示分析黎曼张量的特征值,这使我们能够以不变的方式找到可能存在排斥效应的区域。此外,我们对运动方程进行数值求解以显示阴影、爱因斯坦环和引力透镜,以建立这种排斥效应的可能特征。我们发现随着$q$变小,爱因斯坦环减小,但形状与史瓦西黑洞情况相同。然而,对于 $q$ 低于或等于 $-0.5$ 的值,排斥引力效应出现在靠近致密物体的引力透镜中,在那里系统似乎发生了对初始条件的强烈依赖。可能存在排斥效应的区域。此外,我们对运动方程进行数值求解以显示阴影、爱因斯坦环和引力透镜,以建立这种排斥效应的可能特征。我们发现随着$q$变小,爱因斯坦环减小,但形状与史瓦西黑洞情况相同。然而,对于 $q$ 低于或等于 $-0.5$ 的值,排斥引力效应出现在靠近致密物体的引力透镜中,在那里系统似乎发生了对初始条件的强烈依赖。可能存在排斥效应的区域。此外,我们对运动方程进行数值求解以显示阴影、爱因斯坦环和引力透镜,以建立这种排斥效应的可能特征。我们发现随着$q$变小,爱因斯坦环减小,但形状与史瓦西黑洞情况相同。然而,对于 $q$ 低于或等于 $-0.5$ 的值,排斥引力效应出现在靠近致密物体的引力透镜中,在那里系统似乎发生了对初始条件的强烈依赖。爱因斯坦环减小,但形状与史瓦西黑洞情况相同。然而,对于 $q$ 低于或等于 $-0.5$ 的值,排斥引力效应出现在靠近致密物体的引力透镜中,在那里系统似乎发生了对初始条件的强烈依赖。爱因斯坦环减小,但形状与史瓦西黑洞情况相同。然而,对于 $q$ 低于或等于 $-0.5$ 的值,排斥引力效应出现在靠近致密物体的引力透镜中,在那里系统似乎发生了对初始条件的强烈依赖。
更新日期:2020-12-10
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