A two-dimensional integral identity is derived for a general asymptotically flat four-dimensional spacetime, providing a generalization of the `virial' identity obtained by Bonazzola for the stationary axisymmetric case. It is applied to show that some spatial component of the stress--energy tensor must be positive in some (if not all) points of a static stellar model. This identity has also proved to be useful for checking numerical solutions of Einstein's equation describing rotating neutron stars.
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Bonazzola et al. (1994) studied this question.
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