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Stationary circularly symmetric solutions of General Relativity with negativecosmological constant coupled to the Maxwell field are analyzed in threespacetime dimensions. Taking into account that the fall-off of the fields isslower than the standard one for a localized distribution of matter, it isshown that, by virtue of a suitable choice of the electromagnetic Lagrangemultiplier, the action attains a bona fide extremum provided the asymptoticform of the electromagnetic field fulfills a nontrivial integrabilitycondition. As a consequence, the mass and the angular momentum becomeautomatically finite, without the need of any regularization procedure, andthey generically acquire contributions from the electromagnetic field.Therefore, unlike the higher-dimensional case, it is found that the precisevalue of the mass and the angular momentum explicitly depends on the choice ofboundary conditions. It can also be seen that requiring compatibility of theboundary conditions with the Lorentz and scaling symmetries of the class ofstationary solutions, singles out a very special set of "holographic boundaryconditions" that is described by a single parameter. Remarkably, in starkcontrast with the somewhat pathological behaviour found in the standard case,for the holographic boundary conditions (i) the energy spectrum of anelectrically charged (rotating) black hole is nonnegative, and (ii) for a fixedvalue of the mass, the electric charge is bounded from above.

Conserved charges and black holes in the Einstein-Maxwell theory on AdS$_{3}$ reconsidered