The recent observation that black holes in certain Einstein-Maxwell-dilaton (EMD) theories can violate the entropy super-additivity led to the suggestion that these black holes might repel each other. In this paper, we consider EMD theories with two Maxwell fields A i , with general exponential couplings exp ( a i ? ) in their kinetic terms. We calculate the gravielectrostatic force between charged black holes ( m 1 , e 1 ) and ( M 2 , Q 2 ) ; the former is sufficiently small and can be treated as a pointlike object. We find there is a potential barrier caused by the dilaton coupling at r 0 outside the black hole horizon r + , provided that ? a 1 a 2 > 2 ( D ? 3 ) / ( D ? 2 ) . As the black hole approaches extremality, both r + and r 0 vanish, the barrier becomes infinitesimally thin but infinitely high, and the two black holes repel each other in the whole space. There is no electrostatic force between them; the dilaton is the antigravity agent. Furthermore we find that the exact constraint on a 1 a 2 can be derived from the requirements that two-charged extremal black holes have a fission bomb like mass formula and the violation of entropy super-additivity can occur. The two very different approaches give a consistent picture of the black hole repulsion.
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机译：最近的观察发现，某些爱因斯坦-麦克斯韦-迪拉顿（EMD）理论中的黑洞可能违反熵超可加性，这表明这些黑洞可能相互排斥。在本文中，我们考虑具有两个麦克斯韦场A i的EMD理论，它们的动力学术语具有一般指数耦合exp（a i？）。我们计算了带电黑洞（m 1，e 1）和（M 2，Q 2）之间的静电力;前者足够小，可以视为点状对象。我们发现，在黑洞视界r +之外，在r 0处的dilaton耦合会引起势垒，条件是？ a 1 a 2> 2（D？3）/（D？2）。当黑洞接近末端时，r +和r 0都消失，势垒变得无限薄而无限高，并且两个黑洞在整个空间中相互排斥。它们之间没有静电力。 dilaton是抗重力剂。此外，我们发现对1 a 2的精确约束可以从如下条件得出：双电荷的极黑洞具有类似于质量公式的裂变炸弹，并且可能发生熵超可加性的违反。两种截然不同的方法给出了黑洞排斥的一致图像。
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