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The global nonlinear stability of Minkowski space for the Einstein-massive field system and the f(R)-theory of modified gravity LeFloch, Philippe


We consider the initial value problem for the Einstein-massive field system, and for the f(R)-theory of modified gravity, for which the field equations are an extension to the classical Einstein equations. Our main result concerns the nonlinear global stability of Minkowski space- time for both theories. Our proof relies on the Hyperboloidal Foliation Method introduced by the authors to tackle coupled systems of wave-Klein-Gordon equations posed on a curved space (with unknown metric). We are able also to prove that the Cauchy developments of modified gravity converge to those associated with the Einstein equations when the function f(R) approaches R. This is a joint work with Y. Ma (Xi’an) and preprints are available at and ArXiv:1411.4910 and ArXiv:1507.01143.

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