具有黑洞和Kaluza-Klein泡的磁化位形：类Smarr关系和第一定律
Magnetized configurations with black holes and Kaluza-Klein bubbles: Smarr-like relations and first law
摘要：
本文给出了描述黑洞和沿紧维磁化的Kaluza-Klein泡位形的Einstein-Maxwell-Einstein引力理论的一般精确解。我们还利用Noether流方法导出了这些构型的质量和张力第一定律。我们考虑的解是明确的例子，表明在卡鲁扎-克莱因时空中，间隔（棒）结构和电荷（在这里的解中，它们的构造为零）不足以对解进行分类，还需要额外的数据，即磁通量（es）。
英文摘要：
We present a general class of exact solutions in Einstein-Maxwell-dilaton gravity describing configurations of black holes and Kaluza-Klein bubbles magnetized along the compact dimension. Smarr-like relations for the mass and the tension are found. We also derive the mass and tension first law for the configurations under consideration using the Noether current approach. The solutions we consider are explicit examples showing that in Kaluza-Klein spacetimes the interval (rod) structure and the charges (which are zero by construction for the solutions here), are insufficient to classify the solutions and additional data is necessary, namely the magnetic flux(es).
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