We obtain the general static, spherically symmetric solution for the Einstein-Maxwell-dilaton system in four dimensions with a phantom coupling for the dilaton and/or the Maxwell field. This leads to new classes of black hole solutions, with single or multiple horizons. Using the geodesic equations, we analyze the corresponding Penrose diagrams revealing, in some cases, new causal structures.
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Clément et al. (2009) studied this question.
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