2024/08/20 by Sansom, Robert
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2408.10859
In this paper, we investigate the C3-null gluing problem for the Einstein vacuum equations, that is, we consider the null gluing of up to and including third-order derivatives of the metric. In the regime where the characteristic data is close to Minkowski data, we show that this C3-null gluing problem is solvable up to a 20-dimensional space of obstructions. The obstructions correspond to 20 linearly conserved quantities: 10 of which are already present in the C2-null gluing problem analysed by Aretakis, Czimek and Rodnianski, and 10 are novel obstructions inherent to the C3-null gluing problem. The 10 novel obstructions are linearly conserved charges calculated from third-order derivatives of the metric.