Spherically symmetric Einstein-scalar-field equations for wave-like decaying null infinity

Abstract

We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique local solutions and unique global solutions for small initial data. We also generalize Christodoulou's global generalized solutions to the wave-like decaying initial data. We emphasize that this decaying condition is sharp.

42 pages. The structure of the paper is re-arranged to improve the presentation of the paper. The estimates for A1, A2, A3 and A4 (page 19) are improved, which essentially provide the stronger conclusions including r=0 on the local and global existences