Spherically symmetric Einstein-scalar-field equations for wave-like decaying null infinity
General Relativity and Quantum Cosmology
2022-09-05 v2 Analysis of PDEs
Differential Geometry
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.
Keywords
Cite
@article{arxiv.2108.03419,
title = {Spherically symmetric Einstein-scalar-field equations for wave-like decaying null infinity},
author = {Chuxiao Liu and Xiao Zhang},
journal= {arXiv preprint arXiv:2108.03419},
year = {2022}
}
Comments
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