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We study the physical properties of conformally flat initial data for single and binary black-hole configurations obtained using imaging and puncture methods. We investigate how the total mass Mtot of a dataset with two black holes depends on the configuration of linear or angular momentum and separation of the holes. The asymptotic behaviour of Mtot with increasing separation allows us to make conclusions about a nonphysical extra gravitational field introduced in the solutions by the conformally flat approach. We also calculate the spatial distribution of scalar invariants of the Riemann tensor which determine the gravitational tidal forces. For single black-hole configurations, these are compared to the known analytical solutions. Spatial distribution of the invariants allows us to make certain conclusions about the local distribution of the additional field in the numerical datasets.

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Classical and Quantum Gravity

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