Event Horizon of the Monopole-Quadrupole solution: geometric and   thermodynamic properties
  We investigate the general geometric properties of the surface of infinite red-shift corresponding to the event horizon of the static and axisymmetric solution of the Einstein vacuum equations that only possesses mass $M$ and quadrupole moment $Q$. The deformation of the Schwarzschild surface $r=2M$ produced by the quadrupole moment is shown, and the range of values of this multipole moment is specified, which preserves a regular, closed, continuous and differentiable surface. Some thermodynamic consequences and speculations ensuing from our results are discussed. 
J.L. Hernandez-Pastora and L. Herrera
gr-qc astro-ph.SR