A necessary and sufficient condition for York data to specify an asymptotically flat spacetime

This paper studies the conditions under which Cauchy data $\mathrm{(ḡ,\pi ̄,\nu ̄,T̄)}$ for an asymptotically flat spacetime are determined by the freely specifiable York data (g, σ, ν, T) (τ=0), where tr_gσ=0, div_gσ=8πν. It is shown that the space of such σ′s is infinite dimensional. Furthermore,it is shown that (g, σ, ν, T) determine conformally equivalent Cauchy data if and only if g is conformally equivalent to an asymptotically flat metric with nonnegative scalar curvature.