The strength of Einstein's equations

Abstract

The strength of Einstein's empty-space field equations is computed anew and shown to be equal to the amount of initial data required for a local solution of the equations. This same amount of initial data is shown to be precisely that required for a set of 16 unknown first-order differential equations containing 10 field variables and having six identities of second order. The 10 field variables must be functions of second order in the metric coefficients. The 16 field equationsC αβμσ ,α = 0 whereC αβμσ is Weyl's conformal tensor, are shown to have the same properties as those of the unknown equations, suggesting thatC αβμσ = 0 is a satisfactory local first-order formulation of Einstein's second-order empty-space field equations.