The spacetime in the neighborhood of a general isolated black hole
  We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with the horizon as an inner boundary. The spacetime metric and other geometric fields are expanded in a power series in a radial coordinate away from the horizon by solving the characteristic field equations in the Newman-Penrose formalism. This is the first in a series of papers which investigate the near horizon geometry and its physical applications using the isolated horizon framework. 
Badri Krishnan
gr-qc