Mass formula for a stationary axisymmetric configuration and the physical realization of the Kerr metric

Abstract We analyse the expression for the mass of a stationary axisymmetric configuration in general relativity obtained in our previous work [Mod. Phys. Lett. A 10 (1995) 841]. From the generality of our formula and its incompatibility with the corresponding expression in Kerr space-time we argue that a stationary equilibrium distribution of real matter cannot be a source of the Kerr metric.