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According to the no-hair theorem, an astrophysical black hole is uniquelydescribed by only two quantities, the mass and the spin. In this series ofpapers, we investigate a framework for testing the no-hair theorem withobservations of black holes in the electromagnetic spectrum. We formulate ourapproach in terms of a parametric spacetime which contains a quadrupole momentthat is independent of both mass and spin. If the no-hair theorem is correct,then any deviation of the black-hole quadrupole moment from its Kerr value hasto be zero. We analyze in detail the properties of this quasi-Kerr spacetimethat are critical to interpreting observations of black holes and demonstratetheir dependence on the spin and quadrupole moment. In particular, we show thatthe location of the innermost stable circular orbit and the gravitationallensing experienced by photons are affected significantly at even modestdeviations of the quadrupole moment from the value predicted by the no-hairtheorem. We argue that observations of black-hole images, of relativisticallybroadened iron lines, as well as of thermal X-ray spectra from accreting blackholes will lead in the near future to an experimental test of the no-hairtheorem.

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: I. Properties of a Quasi-Kerr Spacetime