A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a $spatial$ singularity at the origin $ r = 0 $ is found. These solutions are parametrized by a real valued parameter $ \lambda$ (ranging from $ 0 $ to $ \infty$) and such that the radial horizon's location is $displaced$ continuously towards the singularity ($ r = 0 $) as $ \lambda $ increases. In the limit $ \lambda \rightarrow \infty$, the location of the singularity and horizon $merges$ leading to a $null$ singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. Another salient feature of these solutions is that it leads to a modification of the Newtonian potential consistent with the effects of the generalized uncertainty principle (GUP) associated to a minimal length. The field equations due to a delta-function point-mass source at $ r = 0 $ are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions $ D \ge 3 $. The study of the Nonperturbative Renormalization Group flow of the metric $ g_{\mu v} [ k ] $ in terms of the momentum scale $ k $ and its relationship to these family of metrics parametrized by $ \lambda$ deserves further investigation.