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The black hole in the center of the Milky Way, Sgr A*, has the largestmass-to-distance ratio among all known black holes in the Universe. Thisproperty makes Sgr A* the optimal target for testing the gravitational no-hairtheorem. In the near future, major developments in instrumentation will providethe tools for high-precision studies of its spacetime via observations ofrelativistic effects in stellar orbits, in the timing of pulsars, and inhorizon-scale images of its accretion flow. We explore here the prospect ofmeasuring the properties of the black-hole spacetime using all these threetypes of observations. We show that the correlated uncertainties in themeasurements of the black-hole spin and quadrupole moment using the orbits ofstars and pulsars are nearly orthogonal to those obtained from measuring theshape and size of the shadow the black hole casts on the surrounding emission.Combining these three types of observations will, therefore, allow us to assessand quantify systematic biases and uncertainties in each measurement and leadto a highly accurate, quantitative test of the gravitational no-hair theorem.

A Quantitative Test of the No-Hair Theorem with Sgr A* using stars, pulsars, and the Event Horizon Telescope