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The Event Horizon Telescope (EHT) has imaged the shadow of the supermassiveblack hole in M87. A library of general relativistic magnetohydrodynamics(GMRHD) models was fit to the observational data, providing constraints onblack hole parameters. We investigate how much better future experiments canrealistically constrain these parameters and test theories of gravity. Wegenerate realistic synthetic 230 GHz data from representative input modelstaken from a GRMHD image library for M87, using the 2017, 2021, and an expandedEHT array. The synthetic data are run through a data reduction pipeline used bythe EHT. Additionally, we simulate observations at 230, 557, and 690 GHz withthe Event Horizon Imager (EHI) Space VLBI concept. Using one of the EHTparameter estimation pipelines, we fit the GRMHD library images to thesynthetic data and investigate how the black hole parameter estimations areaffected by different arrays and repeated observations. Repeated observationsplay an important role in constraining black hole and accretion parameters asthe varying source structure is averaged out. A modest expansion of the EHTalready leads to stronger parameter constraints. High-frequency observationsfrom space rule out all but ~15% of the GRMHD models in our library, stronglyconstraining the magnetic flux and black hole spin. The 1$\sigma$ constraintson the black hole mass improve by a factor of five with repeated high-frequencyspace array observations as compared to observations with the current groundarray. If the black hole spin, magnetization, and electron temperaturedistribution can be independently constrained, the shadow size for a givenblack hole mass can be tested to ~0.5% with the EHI, which allows tests ofdeviations from general relativity. High-precision tests of the Kerr metricbecome within reach from observations of the Galactic Center black holeSagittarius A*.

Black hole parameter estimation with synthetic Very Long Baseline Interferometry data from the ground and from space