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The well-known BTZ black hole solution of (2+1) Einstein's gravity, in thepresence of a cosmological constant, is treated both at the classical andquantum level. Classically, the imposition of the two manifest local Killingfields of the BTZ geometry at the level of the full action results in amini-superspace constraint action with the radial coordinate playing the roleof the independent dynamical variable. The Noether symmetries of this reducedaction are then shown to completely determine the classical solution space,without any further need to solve the dynamical equations of motion. At aquantum mechanical level, all the admissible sets of the quantum counterpartsof the generators of the above mentioned symmetries are utilized assupplementary conditions acting on the wave-function. These additionalrestrictions, in conjunction with the Wheeler-DeWitt equation, help todetermine (up to constants) the wave-function which is then treatedsemiclassically, in the sense of Bohm. The ensuing space-times are, eitheridentical to the classical geometry, thus exhibiting a good correlation of thecorresponding quantization to the classical theory, or are less symmetric butexhibit no Killing or event horizon and no curvature singularity, thusindicating a softening of the classical conical singularity of the BTZgeometry.

Canonical Quantization of the BTZ Black Hole using Noether Symmetries