Black Holes That Repel

H. Lu; Zhao-Long Wang; Qing-Qing Zhao

doi:10.1103/PhysRevD.99.101502

paper

Black Holes That Repel

arXiv:1901.02894 · doi:10.1103/PhysRevD.99.101502

Abstract

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 $exp (a_{i} ϕ)$ in their kinetic terms. We calculate the gravi-electrostatic 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 point-like object. We find there is a potential barrier caused by the dilaton coupling at $r_{0}$ outside the back 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 fusion 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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Black Holes That Repel

Abstract

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