The quality factor of approximate solutions of Einstein's equations (Q1096199)

The paper gives a criterion to measure how good an approximate solution of Einstein's field equations is, through the definition of a scalar, a quality factor Q, without knowing the exact solution which is being approximated. The quality factor is defined at a given point and associated to a time-like congruence as it can be identified with the state of motion of the physical frame. Q measures in some sense the quality of an approximate solution for different time-like congruences. An application of the quality factor concept for three different approximate solutions is done, however, the results obtained show that Q cannot be always a reliable test to decide when and where an approximation is acceptable and then whether Q is an interesting quantity to be considered. In any case Q brings some insight into the quality of an approximate solution of Einstein's vacuum equations and towards the definition of a quality factor.