Stability for small data: the drift model of the conformal method
Abstract
The conformal method in general relativity aims at successfully parametrising the set of all initial data associated with globally hyperbolic spacetimes. One such mapping was suggested by Maxwell D (2014 Initial data in general relativity described by expansion, conformal deformation and drift (arXiv:1407.1467)). For closed manifolds, I verify that the solutions of the corresponding conformal system are stable, in the sense that they present a priori bounds under perturbations of the system's coefficients. This result holds in dimensions 3 ⩽ n ⩽ 5, when the metric is conformally flat, the drift is small. A scalar field with suitably high potential is considered in this case.
- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- October 2020
- DOI:
- 10.1088/1361-6382/abadb0
- arXiv:
- arXiv:2001.01586
- Bibcode:
- 2020CQGra..37s5028V
- Keywords:
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- general relativity;
- constraint equations;
- mathematical physics;
- Mathematics - Analysis of PDEs;
- Mathematical Physics