On a class of global characteristic problems for the Einstein vacuum equations with small initial data

Abstract

We study a class of global characteristic problems for the Einstein vacuum equations with small initial data. In a previous work [Caciotta and Nicolò, “Global characteristic problem for Einstein vacuum equations with small initial data: (I) The initial data constraints,” Journal of Hyperbolic Differential Equations (JHDE) 2, 201 (2005)], denoted by Paper I, our attention was focused on prescribing the initial data satisfying the constraints imposed by the characteristic problem. In this paper we show how the global existence result can be achieved. This result is heavily based on the global results of Christodoulou and Klainerman [The Global Nonlinear Stability of the Minkowski Space, Princeton Mathematical Series Vol. 41 (Princeton University Press, Princeton, NJ, 1993)] and Klainerman and Nicolò [The Evolution Problem in General Relativity, Progress in Mathematical Physics Vol. 25 (Birkhauser, Boston, MA, 2002)].