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In this work, we investigate the embedding of a four-dimensional spherically symmetric metric in a six dimensional bulk. By using the Nash-Greene theorem, the additional $SO(2)$ symmetry of the two space-like extra-dimensions induces the appearance of horizons of a lukewarm charged black hole. Accordingly, an emerged mass-dependent cosmological constant is obtained with a prediction with a bound for the mass and minimal charge.doi:10.20944/preprints201903.0112.v1 fatcat:ybvzwcy6efaexl4fd3l6yboxja