Batic D, Debru N B, Nowakowski M
Department of Mathematics, Khalifa University of Science and Technology, Main Campus, Abu Dhabi, United Arab Emirates.
Department of Physics, Khalifa University of Science and Technology, Main Campus, Abu Dhabi, United Arab Emirates.
Heliyon. 2023 Sep 7;9(9):e19828. doi: 10.1016/j.heliyon.2023.e19828. eCollection 2023 Sep.
In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our results further reinforce the importance and special character of axisymmetric solutions in general relativity and highlight the role of integral transforms methods in solving complex problems in this field. We compare our results to already existing solutions which exhibit the same type of singularities. In this context we notice that most known axial-symmetric solutions possess naked singularities. A discussion of characteristic features of the newly found metrics, e.g., blueshift and the geometry of the singularities, is given.
在本文中，我们给出了爱因斯坦场方程新的轴对称和反射对称真空解。它们是用汉克尔积分变换法得到的，并且所有这三个解都呈现出裸奇点。我们的结果进一步强化了轴对称解在广义相对论中的重要性和特殊性质，并突出了积分变换方法在解决该领域复杂问题中的作用。我们将我们的结果与已有的呈现相同类型奇点的解进行了比较。在这种情况下，我们注意到大多数已知的轴对称解都具有裸奇点。文中给出了对新发现度规的特征的讨论，例如蓝移和奇点的几何形状。
