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The four-dimensional Einstein-Maxwell action is modified by introducing a 'non-minimal coupling' between the electromagnetic field strength and the spacetime curvature. This is partly motivated by recent results on dimensional reduction of higherdimensional unified theories.We study the corresponding field equations in the case of static and spherically symmetric field configurations, and classify the solutions without magnetic charge according to their global properties It is shown that asymptotically flat black hole solutions have positive ADM mass and satisfy similar relations between mass and charge as the Reissner-Weyl-Nordstrdm solution of the minimally coupled Einstein-Maxwell equations.

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