ON THE QUESTION OF CLASSICAL AXIONIC HAIR IN THE MINIMAL COUPLING THEORY OF GRAVITY AND KALB-RAMOND FIELD

Under axisymmetry invariance and the invariance of simultaneous invers ion of time and azimuthal angle, we show that the axionic Kerr black h ole is the unique stationary solution of the minimal coupling theory o f gravity and the Kalb-Ramond field, which has a regular event horizon , is asymptotically flat and has a finite axion field strength at the event horizon. However, the axionic black hole with a surface gravity that vanishes everywhere except on the symmetry axis is physically unr ealistic. Therefore, we may conclude that there is no classical hair i n the theory in which gravity is minimally coupled to the Kalb-Ramond field.