In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr–Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr–Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson–Trautman coordinates to Bondi–Sachs, including the perturbation term of the boosted Robinson–Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy–momentum tensor the boosted Kerr–Newman solution. To this end, we consider the electromagnetic energy–momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy–momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr–Newman metric. To proceed, we examine the causal structure of the boosted Kerr–Newman black hole in Bondi–Sachs coordinates as in a preferred timelike foliation. We show that the ultimate effect of a nonvanishing charge is to shrink the overall size of the event horizon and ergosphere areas when compared to the neutral boosted Kerr black holes. Considering the preferred timelike foliation we obtain the electromagnetic fields for a proper nonrotating frame of reference. We show that while the electric field displays a pure radial behavior, the magnetic counterpart develops an involved structure with two intense lobes of the magnetic field observed in the direction opposite to the boost.

中文翻译：

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增强的 Kerr-Newman 黑洞


在本文中，我们获得了爱因斯坦场方程的新解，它描述了在未来零无穷大处相对于洛伦兹框架的增强 Kerr-Newman 黑洞。为了简化我们的分析，我们考虑了一种特定的配置，其中助推与黑洞角动量对齐。提升的 Kerr-Newman 黑洞是考虑到 Robinson-Trautman 坐标到 Bondi-Sachs 的完全渐近洛伦兹变换，包括提升的 Robinson-Trautman 度量的扰动项。为了验证度量的最终形式确实是爱因斯坦场方程的解，我们评估了相应的能量-动量张量，即提升的 Kerr-Newman 解。为此，我们考虑了用 Kerr 提升度量构建的电磁能量-动量张量及其类似时间的杀伤向量。我们表明，这样获得的 Papapetrou 场产生了一个能量-动量张量，该张量满足 Kerr-Newman 度量的爱因斯坦场方程，最高可达 4 阶。为了继续，我们研究了 Bondi-Sachs 坐标中增强的 Kerr-Newman 黑洞的因果结构，就像在首选的类时间叶子中一样。我们表明，与中性增强的克尔黑洞相比，非消失电荷的最终效果是缩小事件视界和反流层区域的整体大小。考虑到首选的类时叶，我们获得了适当的非旋转参考系的电磁场。我们表明，虽然电场表现出纯径向行为，但磁场会发展出一个复杂的结构，在与助推相反的方向上观察到两个强烈的磁场波瓣。