Asymptotically shearfree congruences in (2,2) spacetimes and Burgers' equation

Abstract

The paper proves that any asymptotically shearfree congruence at the conformal infinity (scri) in a (2,2)-signature spacetime is determined locally by a solution to the pair of forced inviscid Burgers' equations L_u+LL_x=σ(u,x,y,L) and M_u+MM_y=σ'(u,x,y,M) where u,x,y are Bondi coordinates of scri. The functions σ and σ' are determined naturally by the projective structure on the α and β surfaces that foliate scri.

13 pages