Harrison metrics for the Schwarzschild black hole

Based on the hidden conformal symmetry, some authors have proposed a Harrison metric for the Schwarzschild black hole. We give a procedure which can generate a family of Harrison metrics starting from a general set of SL(2, R) vector fields. By analogy with the subtracted geometry of the Kerr black hole, we find a new Harrison metric for the Schwarzschild case. Its conformal generators are also investigated using the Killing equations in the near-horizon limit.