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The $$C^3$$-Null Gluing Problem: Linear and Nonlinear Analysis
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Abstract
In this paper, we investigate the
$$C^3$$
C
3
-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
$$C^3$$
C
3
-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
$$C^2$$
C
2
-null gluing problem analysed by Aretakis, Czimek and Rodnianski [2–4], and 10 are novel obstructions inherent to the
$$C^3$$
C
3
-null gluing problem. The 10 novel obstructions are linearly conserved charges calculated from third-order derivatives of the metric.
Title: The $$C^3$$-Null Gluing Problem: Linear and Nonlinear Analysis
Description:
Abstract
In this paper, we investigate the
$$C^3$$
C
3
-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
$$C^3$$
C
3
-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
$$C^2$$
C
2
-null gluing problem analysed by Aretakis, Czimek and Rodnianski [2–4], and 10 are novel obstructions inherent to the
$$C^3$$
C
3
-null gluing problem.
The 10 novel obstructions are linearly conserved charges calculated from third-order derivatives of the metric.
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