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Annales Henri Poincaré

, Volume 16, Issue 9, pp 2059–2129 | Cite as

Conformally Covariant Systems of Wave Equations and their Equivalence to Einstein’s Field Equations

  • Tim-Torben PaetzEmail author
Article

Abstract

We derive, in 3 + 1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich’s conformal field equations. We analyse their equivalence to Einstein’s vacuum field equations when appropriate constraint equations are satisfied by the initial data. As an application, the characteristic initial value problem for the Einstein equations with data on past null infinity is reduced to a characteristic initial value problem for wave equations with data on an ordinary light-cone.

Keywords

Wave Equation Constraint Equation Initial Surface Weyl Tensor Null Hypersurface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Gravitational PhysicsUniversity of ViennaViennaAustria

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